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fin.c
1/***************************************************************************
2 fin.c - description
3 -------------------
4 begin : Thursday June 15 2000
5 email : tboldt@attglobal.net
6 Author : Terry D. Boldt
7 ***************************************************************************/
8
9/***************************************************************************
10 * *
11 * This program is free software; you can redistribute it and/or modify *
12 * it under the terms of the GNU General Public License as published by *
13 * the Free Software Foundation; either version 2 of the License, or *
14 * (at your option) any later version. *
15 * *
16 ***************************************************************************/
17
18/*
19 * Functions to compute financial equations and amortization schedules
20 * 6-15-2000
21 *
22 */
23
24/*
25 * Financial Calculator
26 *
27 * This version for use WITH ANSI.SYS display driver
28 *
29 * This is a complete financial computation utility to solve for the
30 * five * standard financial values: n, %i, PV, PMT and FV
31 *
32 * n == number of payment periods
33 * %i == nominal interest rate, NAR, charged
34 * PV == Present Value
35 * PMT == Periodic Payment
36 * FV == Future Value
37 *
38 * In addition, two additional parameters may be specified:
39 *
40 * 1) Compounding Frequency per year, CF. The compounding frequency
41 * per year may be discrete or continuous and may be different from
42 * the Payment Frequency per year
43 *
44 * 2) Payment Frequency per year, PF. Payments may be made at the
45 * beginning or the end of the payment period.
46 *
47 * When an amortization schedule is desired, the financial
48 * transaction Effective Date, ED, and Initial Payment Date, IP, must
49 * also be entered.
50 *
51 * Canadian and European style mortgages can be handled in a simple,
52 * straight-forward manner. Standard financial sign conventions are
53 * used:
54 *
55 * "Money paid out is Negative, Money received is Positive"
56 *
57 * Time value of money:
58 *
59 * If you borrow money, you can expect to pay rent or interest for its use;
60 * conversely you expect to receive rent interest on money you loan or invest.
61 * When you rent property, equipment, etc., rental payments are normal; this
62 * is also true when renting or borrowing money. Therefore, money is
63 * considered to have a "time value". Money available now, has a greater value
64 * than money available at some future date because of its rental value or the
65 * interest that it can produce during the intervening period.
66 *
67 * Simple Interest:
68 *
69 * If you loaned $800 to a friend with an agreement that at the end of one
70 * year he would would repay you $896, the "time value" you placed on your
71 * $800 (principal) was $96 (interest) for the one year period (term) of the
72 * loan. This relationship of principal, interest, and time (term) is most
73 * frequently expressed as an Annual Percentage Rate (APR). In this case the
74 * APR was 12.0% [(96/800)*100]. This example illustrates the four basic
75 * factors involved in a simple interest case. The time period (one year),
76 * rate (12.0% APR), present value of the principal ($800) and the future
77 * value of the principal including interest ($896).
78 *
79 * Compound Interest:
80 *
81 * In many cases the interest charge is computed periodically during the term
82 * of the agreement. For example, money left in a savings account earns
83 * interest that is periodically added to the principal and in turn earns
84 * additional interest during succeeding periods. The accumulation of interest
85 * during the investment period represents compound interest. If the loan
86 * agreement you made with your friend had specified a "compound interest
87 * rate" of 12% (compounded monthly) the $800 principal would have earned
88 * $101.46 interest for the one year period. The value of the original $800
89 * would be increased by 1% the first month to $808 which in turn would be
90 * increased by 1% to 816.08 the second month, reaching a future value of
91 * $901.46 after the twelfth iteration. The monthly compounding of the nominal
92 * annual rate (NAR) of 12% produces an effective Annual Percentage Rate (APR)
93 * of 12.683% [(101.46/800)*100]. Interest may be compounded at any regular
94 * interval; annually, semiannually, monthly, weekly, daily, even continuously
95 * (a specification in some financial models).
96 *
97 * Periodic Payments:
98 *
99 * When money is loaned for longer periods of time, it is customary for the
100 * agreement to require the borrower to make periodic payments to the lender
101 * during the term of the loan. The payments may be only large enough to repay
102 * the interest, with the principal due at the end of the loan period (an
103 * interest only loan), or large enough to fully repay both the interest and
104 * principal during the term of the loan (a fully amoritized loan). Many loans
105 * fall somewhere between, with payments that do not fully cover repayment of
106 * both the principal and interest. These loans require a larger final payment
107 * (balloon) to complete their amortization. Payments may occur at the
108 * beginning or end of a payment period. If you and your friend had agreed on
109 * monthly repayment of the $800 loan at 12% NAR compounded monthly, twelve
110 * payments of $71.08 for a total of $852.96 would be required to amortize the
111 * loan. The $101.46 interest from the annual plan is more than the $52.96
112 * under the monthly plan because under the monthly plan your friend would not
113 * have had the use of $800 for a full year.
114 *
115 * Financial Transactions:
116 *
117 * The above paragraphs introduce the basic factors that govern most
118 * financial transactions; the time period, interest rate, present value,
119 * payments and the future value. In addition, certain conventions must be
120 * adhered to: the interest rate must be relative to the compounding frequency
121 * and payment periods, and the term must be expressed as the total number of
122 * payments (or compounding periods if there are no payments). Loans, leases,
123 * mortgages, annuities, savings plans, appreciation, and compound growth are
124 * among the many financial problems that can be defined in these terms. Some
125 * transactions do not involve payments, but all of the other factors play a
126 * part in "time value of money" transactions. When any one of the five (four
127 * - if no payments are involved) factors is unknown, it can be derived from
128 * formulas using the known factors.
129 *
130 * Standard Financial Conventions Are:
131 *
132 * Money RECEIVED is a POSITIVE value and is represented by an arrow
133 * above * the line
134 *
135 * Money PAID OUT is a NEGATIVE value and is represented by an arrow
136 * below * the line.
137 *
138 * If payments are a part of the transaction, the number of payments
139 * must * equal the number of periods (n).
140 *
141 * Payments may be represented as occurring at the end or beginning of
142 * the * periods.
143 *
144 * Diagram to visualize the positive and negative cash flows (cash
145 * flow * diagrams):
146 *
147 * Amounts shown above the line are positive, received, and amounts
148 * shown below the line are negative, paid out.
149 *
150 * 1)
151 * FV*
152 * 1 2 3 4 . . . . . . . . . n │
153 * Period ┌───┴───┴───┴───┴───┴───┴───┴───┴───┴───┴───┴───┴───┴───┘
154 * │
155 *
156 * PV
157 *
158 * Appreciation
159 * Depreciation
160 * Compound Growth
161 * Savings Account
162 *
163 * ****************************************************************************
164 *
165 * 2) FV
166 * PV = 0
167 * │
168 * Period ┌───┬───┬───┬───┬───┬───┬───┬───┬───┬───┬───┬───┬───┬───┘
169 * │ 1 │ 2 │ 3 │ 4 │ . │ . │ . │ . │ . │ . │ . │ . │ . │ n
170 *
171 * PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT
172 *
173 * Annuity (series of payments)
174 * Pension Fund
175 * Savings Plan
176 * Sinking Fund
177 *
178 * ****************************************************************************
179 *
180 * 3)
181 * PV
182 * │ FV=0
183 * Period └───┬───┬───┬───┬───┬───┬───┬───┬───┬───┬───┬───┬───┬───┐
184 * 1 │ 2 │ 3 │ 4 │ . │ . │ . │ . │ . │ . │ . │ . │ . │ n │
185 *
186 * PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT
187 *
188 * Amortization
189 * Direct Reduction Loan
190 * Mortgage (fully amortized)
191 *
192 * ****************************************************************************
193 *
194 * 4)
195 * FV*
196 * PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT │ +
197 * PMT
198 * 1 │ 2 │ 3 │ 4 │ . │ . │ . │ . │ . │ . │ . │ . │ . │ n │
199 * Period ┌───┴───┴───┴───┴───┴───┴───┴───┴───┴───┴───┴───┴───┴───┘
200 * │
201 *
202 * PV
203 *
204 * Annuity
205 * Lease (with buy back or residual)*
206 * Loan or Mortgage (with balloon)*
207 *
208 * ****************************************************************************
209 *
210 * First lets discuss interest before discussing the financial
211 * equation. Most financial transactions utilize a nominal interest
212 * rate, NAR, i.e., the interest rate per year. The NAR must be
213 * converted to the interest rate per payment interval and the
214 * compounding accounted for before it can be used in computing an
215 * interest payment. After this conversion process, the interest
216 * used is the effective interest rate, EIR. In converting NAR to
217 * EIR, there are two concepts to discuss first, the Compounding
218 * Frequency and the Payment Frequency and * whether the interest is
219 * coumpounded in discrete intervals or continuously. The
220 * compounding Frequency, CF, is simply the number of times per
221 * year, the monies in the financial transaction are compounded. In
222 * the U.S., monies are usually compounded daily on bank deposits,
223 * and monthly on loans. Sometimes Long term deposits are compounded
224 * quarterly or weekly.
225 *
226 * The Payment Frequency, PF, is simply how often during a year
227 * payments are made in the transaction. Payments are usually
228 * scheduled on a regular basis and can be made at the beginning or
229 * end of the payment period. If made at the beginning of the
230 * payment period, interest must be applied to the payment as well
231 * as any previous money paid or money still owed.
232 *
233 * Normal values for CF and PF are:
234 * 1 == annual
235 * 2 == semi-annual
236 * 3 == tri-annual
237 * 4 == quaterly
238 * 6 == bi-monthly
239 * 12 == monthly
240 * 24 == semi-monthly
241 * 26 == bi-weekly
242 * 52 == weekly
243 * 360 == daily
244 * 365 == daily
245 *
246 * a) the Compounding Frequency per year, CF, need not be identical
247 * to the Payment Frequency per year, PF, and/or,
248 *
249 * b) Interest may be compounded in either discrete intervals or continuously
250 * compounded.
251 *
252 * c) Also, payments may be made at the beginning of the payment
253 * period or at the end of the payment period.
254 *
255 * CF and PF are defaulted to 1. The default is for discrete interest
256 * intervals and payments are defaulted to the end of the payment
257 * period.
258 *
259 * When a solution for n, PV, PMT or FV is required, the nominal interest
260 * rate, i, must first be converted to the effective interest rate per payment
261 * period. This rate, ieff, is then used to compute the selected variable. To
262 * convert i to ieff, the following expressions are used:
263 *
264 * Discrete interest periods:
265 *
266 * 19) ieff = (1 + i/CF)^(CF/PF) - 1
267 *
268 * Continuous Interest
269 *
270 * 20) ieff = e^(i/PF) - 1 = exp(i/PF) - 1
271 *
272 * When interest is computed, the computation produces the effective interest
273 * rate, ieff. This value must then be converted to the nominal interest rate.
274 * Function _I below returns the nominal interest rate NOT the effective
275 * interest rate. ieff is converted to i using the following expressions:
276 *
277 * Discrete Case:
278 *
279 * i = CF*[(1+ieff)^(PF/CF) - 1]
280 *
281 * Continuous Case:
282 *
283 * i = ln[(1+ieff)^PF]
284 *
285 * ****************************************************************************
286 *
287 * NOTE: in the equations below for the financial transaction, all
288 * interest rates are the effective interest rate, ieff. The symbol
289 * will be shortned to just 'i'.
290 *
291 * ****************************************************************************
292 *
293 * The basic financial equation used is:
294 *
295 * 1) PV*(1 + i)^n + PMT*(1 + iX)*[(1+i)^n - 1]/i + FV = 0
296 * Where: X = 0 for end of period payments, and
297 * X = 1 for beginning of period payments
298 *
299 * ****************************************************************************
300 *
301 * NOTE: this equation is derived in the following manner:
302 *
303 * Start with the basic equation to find the balance or Present
304 * Value, PV[1], after one payment period. Note PV[1] is the Present
305 * value after on payment and PV[0] is the initial Present
306 * Value. PV[0] will be shortened to just PV.
307 *
308 * The interest due at the end of the first payment period is:
309 *
310 * ID[1] = (PV + X * PMT) * i
311 * where: X = 0 for end of period payments, and
312 * X = 1 for beginning of period payments.
313 *
314 * Thus:
315 * PV[1] = PV + (PMT + ID[1])
316 * = PV + (PMT + (PV + X * PMT) * i)
317 * = PV * (1 + i) + PMT * (1 + Xi)
318 *
319 * This equation works for all of the money diagrams shown
320 * above. The Present Value, money received or paid, is modified by
321 * a payment made at the beginning of a payment period and
322 * multiplied by the effective interest rate to compute the interest
323 * due during the payment period. The interest due is then added to
324 * the payment to obtain the amount to be added to the Present Value
325 * to compute the new Present Value.
326 *
327 * For diagram 1): PV < 0, PMT == 0, PV[1] < 0
328 * For diagram 2): PV == 0, PMT < 0, PV[1] < 0
329 * For Diagram 3): PV > 0, PMT < 0, PV[1] >= 0 or PV[1] <= 0
330 * For Diagram 4): PV < 0, PMT > 0, PV[1] <= 0 or PV[1] >= 0
331 *
332 * X may be 0 or 1 for any diagram.
333 *
334 * For the standard loan, PV is the money borrowed, PMT is the
335 * periodic payment to repay the loan and i is the effective
336 * interest rate agreed upon.
337 *
338 * To calculate the Present Value after the second payment period,
339 * the above calculation is applied iteratively to PV_1:
340 *
341 * PV[2] = PV[1] + (PMT + (PV[1] + X * PMT) * i)
342 * = PV[1] * (1 + i) + PMT * (1 + iX)
343 * = (PV * (1 + i) + PMT * (1 + iX)) * (1 + i) + PMT * (1 + iX)
344 * = PV * (1 + i)^2 + PMT * (1 + iX) * (1 + i)
345 * + PMT * (1 + iX)
346 *
347 * Similarly:
348 *
349 * PV[3] = PV[2] + (PMT + (PV[2] + X * PMT) * i)
350 * = PV[2] * (1 + i) + PMT * (1 + iX)
351 * = PV * (1 + i)^2 + PMT * (1 + iX) * (1 + i)
352 * + PMT * (1+ iX)) * ( 1 + i)
353 * + PMT * (1+ iX)
354 * = PV * (1 + i)^3 + PMT * (1 + iX) * (1 + i)^2
355 * + PMT * (1 + iX) * (1 + i)^2
356 * + PMT * (1 + iX) * (1 + i)
357 * + PMT * (1 + iX)
358 *
359 * And for the n'th payment:
360 *
361 * PV[n] = PV[n-1] + (PMT + (PV[n-1] + X * PMT) * i)
362 * PV[n] = PV * (1 + i)^n + PMT * (1 + iX) * (1 + i)^(n-1)
363 * + PMT * (1 + iX) * (1 + i)^(n-2) +
364 * .
365 * .
366 * .
367 * + PMT * (1 + iX) * (1 + i)
368 * + PMT * (1 + iX)
369 * PV[n] = PV * (1 + i)^n + PMT * (1 + iX) * [(1 + i)^(n-1) + ...
370 * + (1 + i) + 1]
371 *
372 * ****************************************************************************
373 *
374 * The sum of the finite series:
375 *
376 * 1 + k + (k^2) + (k^3) + ... + (k^n) = (1-k^(n+1))/(1-k)
377 *
378 * as can be seen by the following. Let S(n) be the series sum. Then
379 *
380 * S(n) - k * S(n) = 1 - k^(n+1)
381 *
382 * and solving for S(n):
383 *
384 * S(n) = [1-k^(n+1)]/[1-k] = 1 + k + (k^2) + (k^3) + ... + (k^n)
385 *
386 * ****************************************************************************
387 *
388 * PV[n] = PV * (1 + i)^n + PMT * (1 + iX) * [(1 + i)^(n-1) + ...
389 * + (1 + i) + 1]
390 * = PV * (1 + i)^n + PMT * (1 + iX) * [1 - (1 + i)^n]/[1 - (1 + i)]
391 * = PV * (1 + i)^n + PMT * (1 + iX) * [1 - (1 + i)^n]/[-i]
392 * = PV * (1 + i)^n + PMT * (1 + iX) * [(1 + i)^n - 1]/i
393 *
394 * The formaula for PV[n] can be proven using mathematical induction.
395 *
396 * or:
397 *
398 * PV * (1 + i)^n + PMT * [(1 + i)^n - 1]/i - PV[n] = 0
399 *
400 * If after n payments, the remaining balance is repaid as a lump
401 * sum, the lump sum is known as the Future Value, FV[n]. Since
402 * FV[n] is negative if paid and positive if received, FV[n] is the
403 * negative of PV[n]. Since n is assumed to be the last payment,
404 * FV[n] will be shortened to simply FV.
405 *
406 * Setting: FV = -PV[N]
407 *
408 * 1) PV*(1 + i)^n + PMT*(1 + iX)*[(1 + i)^n - 1]/i + FV = 0
409 *
410 * Up to this point, we have said nothing about the value of
411 * PMT. PMT can be any value mutually agreed upon by the lender and
412 * the borrower. From the equation for PV[1]:
413 *
414 * PV[1] = PV + (PMT + (PV + X * PMT) * i),
415 *
416 * Several things can be said about PMT.
417 *
418 * 1. If PMT = PV * i, and X = 0 (end of period payments):
419 *
420 * The payment is exactly equal to the interest due and PV[1] =
421 * PV. In this case, the borrower must make larger future
422 * payments to reduce the balance due, or make a single payment,
423 * after some agreed upon number of payments, with PMT = PV to
424 * completely pay off the loan. This is an interest only payment
425 * with a balloon payment at the end.
426 *
427 * 2. If PMT < PV * i, and X = 0
428 *
429 * The payment is insufficient to cover even the interest charged
430 * and the balance due grows
431 *
432 * 3. If PMT > PV * i, and X = 0
433 *
434 * The payment is sufficient to cover the interest charged with a
435 * residual amount to be applied to reduce the balance due. The
436 * larger the residual amount, the faster the loan is repaid. For
437 * most mortgages or other loans made today, the lender and
438 * borrower agree upon a certain number of repayment periods and
439 * the interest to be charged per payment period. The interest
440 * may be multiplied by 12 and stated as an annual interest
441 * rate. Then the lender and borrower want to compute a periodic
442 * payment, PMT, which will reduce the balance due to zero after
443 * the agreed upon number of payment have been made. If N is the
444 * agreed upon number of periodic payments, then we want to use:
445 *
446 * PV * (1 + i)^N + PMT*(1 +iX)*[(1 + i)^N - 1]/i + FV = 0
447 *
448 * with FV = 0 to compute PMT:
449 *
450 * PMT = -[PV * i * (1 + i)^(N - X)]/[(1 + i)^N - 1]
451 *
452 * The value of PMT computed will reduce the balance due to zero
453 * after N periodic payments.
454 *
455 * ****************************************************************************
456 *
457 *
458 * With a simple alegebraic re-arrangement, The financial Equation becomes:
459 *
460 * 2) [PV + PMT*(1 + iX)/i][(1 + i)^n - 1] + PV + FV = 0
461 *
462 * or
463 *
464 * 3) (PV + C)*A + PV + FV = 0
465 *
466 * where:
467 * 4) A = (1 + i)^n - 1
468 *
469 * 5) B = (1 + iX)/i
470 *
471 * 6) C = PMT*B
472 *
473 * The form of equation 3) simplifies the calculation procedure for all five
474 * variables, which are readily solved as follows:
475 *
476 * 7) n = ln[(C - FV)/(C + PV)]/ln((1 + i)
477 *
478 * 8) PV = -[FV + A*C]/(A + 1)
479 *
480 * 9) PMT = -[FV + PV*(A + 1)]/[A*B]
481 *
482 * 10) FV = -[PV + A*(PV + C)]
483 *
484 * Equations 4), 5) and 6) are computed by functions:
485 *
486 * _A
487 * _B
488 * _C
489 *
490 * respectively. Equations 7), 8), 9) and 10) are computed by functions:
491 *
492 * _N
493 * _PV
494 * _PMT
495 * _FV
496 *
497 * respectively.
498 *
499 * The solution for interest is broken into two cases:
500 *
501 * PMT == 0
502 * i = [FV/PV]^(1/n) - 1
503 *
504 * PMT != 0
505 *
506 * Since equation 3) cannot be solved explicitly for i in this
507 * case, an iterative technique must be employed. Newton's
508 * method, using exact expressions for the function of i and its
509 * derivative, are employed. The expressions are:
510 *
511 * 12) i[k+1] = i[k] - f(i[k])/f'(i[k])
512 * where: i[k+1] == (k+1)st iteration of i
513 * i[k] == kth iteration of i
514 * and:
515 *
516 * 13) f(i) = A*(PV+C) + PV + FV
517 *
518 * 14) f'(i) = n*D*(PV+C) - (A*C)/i
519 *
520 * 15) D = (1 + i)^(n-1) = (A+1)/(1+i)
521 *
522 * To start the iterative solution for i, an initial guess must be made
523 * for the value of i. The closer this guess is to the actual value,
524 * the fewer iterations will have to be made, and the greater the
525 * probability that the required solution will be obtained. The initial
526 * guess for i is obtained as follows:
527 *
528 * if PMT*FV >= 0, then PV case
529 * if PMT*FV < 0, then FV case
530 *
531 * PV case:
532 * | n*PMT + PV + FV |
533 * 16) i[0] = | ----------------|
534 * | n*PV |
535 *
536 * = abs[(n*PMT + PV + FV)/(n*PV)]
537 *
538 * FV case:
539 * a) PV != 0
540 *
541 * | FV - n*PMT |
542 * 17) i[0] = |---------------------------|
543 * | 3*[PMT*(n-1)^2 + PV - FV] |
544 *
545 * = abs[(FV-n*PMT)/(3*(PMT*(n-1)^2+PV-FV))]
546 * b) PV == 0
547 *
548 * | FV + n*PMT |
549 * 18) i[0] = |---------------------------|
550 * | 3*[PMT*(n-1)^2 + PV - FV] |
551 *
552 * = abs[(FV+n*PMT)/(3*(PMT*(n-1)^2+PV-FV))]
553 *
554 * ****************************************************************************
555 * Constant payment to principal loan
556 *
557 * In this loan, each total payment is different, with each
558 * succeeding payment less than the preceding payment. Each payment
559 * is the total of the constant amount to the principal plus the
560 * interest for the period. The constant payment to the principal is
561 * computed as:
562 *
563 * C = -PV / N
564 *
565 * Where PV is the loan amount to be repaid in N payments
566 * (periods). Note that the constant payment to principal could be
567 * any value agreed to by the two parties involved.
568 *
569 * Thus the principal after the first payment is:
570 * PV[1] = PV[0] + C = PV + C
571 * after the second payment, the principal is:
572 * PV[2] = PV[1] + C = PV[0] + 2C
573 * In general, the remaining principal after n payments is:
574 * PV[n] = PV[0] + nC = PV + nC
575 *
576 * If the effective interest per payment period is i, then the
577 * interest for the first payment is:
578 *
579 * I[1] = -i*PV[0] = -i*PV
580 * and for the second:
581 * I[2] = -i * PV[1]
582 * and in general, for the n'th payment the interest is:
583 * I[n] = -i * PV[n-1]
584 * = -i * (PV + (n-1)C)
585 * The total payment for any period, n, is:
586 * P[n] = C + I[n]
587 * = C + i * (PV + (n-1)C)
588 * = C(1 + i) - i * (PV + nC)
589 * The total interest paid to period n is:
590 * T[n] = I[1] + I[2] + I[3] + ... + I[n]
591 * T[n] = sum(j = 1 to n: I[j])
592 * T[n] = sum(j = 1 to n: -i * (PV + (j-1)C))
593 * T[n] = sum(j=1 to n: -i*PV) + sum(j=1 to n: iC) + sum(j=1 to n: -iCj)
594 * T[n] = -i*n*PV + i*n*C - i*C*sum(j=1 to n:j)
595 * sum(j=1 to n:j) = n(n+1)/2
596 * T[n] = -i*n*(PV + C) - i*C*n(n+1)/2
597 * T[n] = -i*n*(PV + (C*(n - 1)/2))
598 *
599 * Note: substituting for C = -PV/N, in the equations for PV[n], I[n],
600 * P[n], and T[n] would give the following equations:
601 *
602 * PV[n] = PV*(1 - n/N)
603 * I[n] = -i*PV*(1 + N - n)/N
604 * P[n] = -i*PV*(2 + N - n)/N
605 * T[n] = -i*n*PV*(2*N - n + 1)/(2*N)
606 *
607 * Using these equations for the calculations would eliminate the
608 * dependence on C, but only if C is always defined as above and
609 * would eliminate the possibility of another value for C. If the
610 * value of C was less than -PV/N then a balloon payment would be
611 * due at the final payment and this is a possible alternative for
612 * some people.
613 *
614 * ****************************************************************************
615 *
616 * Amortization Schedules.
617 *
618 * Financial Transactions have an effective Date, ED, and an Initial Payment
619 * Date, IP. ED may or may not be the same as IP, but IP is always the same
620 * or later than ED. Most financial transaction calculators assume that
621 * IP is equal to ED for beginning of period payments or at the end of the
622 * first payment period for end of period payments.
623 *
624 * This is not always true. IP may be delayed for financial reasons
625 * such as cash flow or accounting calendar. The subsequent payments
626 * then follow the agreed upon periodicity. Since money has a time
627 * value, the "delayed" IP must be accounted for. Computing an
628 * "Effective PV", pve, is one means of handling a delayed IP.
629 *
630 * EDj == the Julian Day Number of ED, and
631 * IPj == the Julian Day Number of IP in the following.
632 *
633 * pve is be computed as:
634 *
635 * pve = pv*(1 + i)^(s*PF/d*CF)
636 *
637 * Where: d = length of the payment period in days, and
638 * s = IPj - EDj - d*X
639 *
640 * Computing an amortization Schedule for a given financial transaction is
641 * simply applying the basic equation iteratively for each payment period:
642 *
643 * PV[n] = PV[n-1] + (PMT + (PV[n-1] + X * PMT) * i)
644 *
645 * At the end of each iteration, PV[n] is rounded to the nearest cent. For
646 * each payment period, the interest due may be computed separately as:
647 *
648 * ID[n] = (PMT + (PV[n-1] + X * PMT) * i)
649 *
650 * and rounded to the nearest cent. PV[n] then becomes:
651 *
652 * PV[n] = PV[n-1] + PMT + ID[n]
653 *
654 * For those cases where a yearly summary only is desired, it is not
655 * necessary to compute each transaction for each payment period,
656 * rather the PV may be computed for the beginning of each year,
657 * PV[yr], and the FV computed for the end of the year, FV[yr]. The
658 * interest paid during the year is the computed as:
659 *
660 * ID[yr] = (NP * PMT) + PV[yr] + FV[yr]
661 *
662 * Since the final payment may not be equal to the periodic payment,
663 * the final payment must be computed separately as follows. Two
664 * derivations are given below for the final payment equation. Both
665 * derivations are given below since one or the other may be clearer
666 * to some readers. Both derivations are essentially the same, they
667 * just have different starting points. The first is the fastest.
668 *
669 * 1) final_pmt == final payment @ payment n == int(n)
670 * from above the basic financial equation:
671 * PV[n] = PV[n-1]*(1 + i) + final_pmt * (1 + iX),
672 * i == effective interest rate
673 *
674 * solving for final_pmt, we have:
675 *
676 * final_pmt * (1 + iX) = PV[n] - PV[n-1]*(1 + i)
677 * = FV[n-1]*(1 + i) - FV[n]
678 * final_pmt = FV[n-1]*(1+i)/(1 + iX) - FV[n]/(1 + iX)
679 *
680 * final_pmt = FV[n-1]*(1 + i) - FV[n],
681 * for X == 0, end of period payments
682 *
683 * = FV[n-1] - FV[n]/(1 + i),
684 * for X == 1, beginning of period payments
685 *
686 * 2) final_pmt == final payment @ payment n == int(n)
687 * i[n] == interest due @ payment n
688 * i[n] = (PV[n-1] + X * final_pmt) * i, i == effective interest rate
689 * = (X * final_pmt - FV[n]) * i
690 *
691 * Now the final payment is the sum of the interest due, plus
692 * the present value at the next to last payment plus any
693 * residual future value after the last payment:
694 *
695 * final_pmt = -i[n] - PV[n-1] - FV[n]
696 * = FV[n-1] - i[n] - FV[n]
697 * = FV[n-1] - (X *final_pmt - FV[n-1])*i - FV[n]
698 * = FV[n-1]*(1 + i) - X*final_pmt*i - FV[n]
699 *
700 * solving for final_pmt:
701 * final_pmt*(1 + iX) = FV[n-1]*(1 + i) - FV[n]
702 * final_pmt = FV[n-1]*(1 + i)/(1 + iX) - FV[n]/(1 + iX)
703 *
704 * final_pmt = FV[n-1]*(1 + i) - FV[n],
705 * for X == 0, end of period payments
706 *
707 * = FV[n-1] - FV[n]/(1 + i),
708 * for X == 1, beginning of period payments
709 *
710 *============================================================================
711 *
712 * The amortization schedule is computed for four different situations:
713 *
714 * 1) The original financial data is used. This ignores any possible
715 * agjustment to the Present value due to any delay in the initial
716 * payment. This is quite common in mortgages where end of period
717 * payments are used and the first payment is scheduled for the end
718 * of the first whole period, i.e., any partial payment period from
719 * ED to the beginning of the next payment period is ignored.
720 *
721 * 2) The original periodic payment is used, the Present Value is
722 * adjusted for the delayed Initial Payment. The total number of
723 * payments remains the same. The final payment is adjusted to bring
724 * the balance into agreement with the agreed upon final Future
725 * Value.
726 *
727 * 3) A new periodic payment is computed based upon the adjusted
728 * Present Value, the agreed originally upon number of total
729 * payments and the agreed upon Future Value. The new periodic
730 * payments are computed to minimize the final payment in accordance
731 * with the Future Value after the last payment.
732 *
733 * 4) The original periodic payment is retained and a new number of
734 * total payments is computed based upon the adjusted Present Value
735 * and the agreed upon Future Value.
736 *
737 * The amortization schedule may be computed and displayed in three manners:
738 *
739 * 1. The payment *, interest paid, principal paid and remaining PV
740 * for each payment period are computed and displayed. At the end of
741 * each year a summary is computed and displayed and the total
742 * interest paid is displayed at the end.
743 *
744 * 2. A summary is computed and displayed for each year. The
745 * interest paid during the year is computed and displayed as well
746 * as the remaining balance at years end. The total interest paid
747 * is displayed at the end.
748 *
749 * 3. An amortization schedule is computed for a common method of
750 * advanced payment of principal is computed and displayed. In this
751 * amortization, the principal for the next payment is computed and
752 * added into the current payment. This method will cut the number
753 * of total payments in half and will cut the interest paid almost
754 * in half. For mortgages, this method of prepayment has the
755 * advantage of keeping the total payments small during the initial
756 * payment periods The payments grow until the last payment period
757 * when presumably the borrower can afford larger payments.
758 *
759 * ===========================================================================
760 * NOTE: For Payment Frequencies, PF, semi-monthly or less, i.e., PF
761 * == 12 or PF == 24, a 360 day calendar year and 30 day month are
762 * used. For Payment Frequencies, PF, greater than semi-monthly, PF
763 * > 24, the actual number of days per year and per payment period
764 * are used. The actual values are computed using the built-in
765 * 'julian_day_number' function
766 *
767 * ****************************************************************************
768 *
769 * Note: in the following examples, the user input is preceded by the
770 * prompt "<>". The result of evaluating the input expression is then
771 * displayed. I have taken the liberty of including comments in the
772 * example input/output sessions by preceding with ' *'. Thus, for
773 * the line: <>n=5 *set number of periods the comment that setting the
774 * number of periods is not really input and the true input is only:
775 * <>n=5
776 *
777 * Example 1: Simple Interest
778 * Find annual simple interest rate (%) for an $800 loan to be repayed at the
779 * end of one year with a single payment of $896.
780 * <>d
781 * <>CF=PF=1
782 * 1.00
783 * <>n=1
784 * 1.00
785 * <>pv=-800
786 * -800.00
787 * <>fv=896
788 * 896.00
789 * <>I
790 * 12.00
791 *
792 * Example 2: Compound Interest
793 * Find the future value of $800 after one year at a nominal rate of 12%
794 * compounded monthly. No payments are specified, so the payment frequency is
795 * set equal to the compounding frequency at the default values.
796 * <>d
797 * <>n=12
798 * 12.00
799 * <>i=12
800 * 12.00
801 * <>pv=-800
802 * -800.00
803 * <>FV
804 * 901.46
805 *
806 * Example 3: Periodic Payment:
807 * Find the monthly end-of-period payment required to fully amortize the loan
808 * in Example 2. A fully amortized loan has a future value of zero.
809 * <>fv=0
810 * 0.00
811 * <>PMT
812 * 71.08
813 *
814 * Example 4: Conventional Mortgage
815 *
816 * Find the number of monthly payments necessary to fully amortize a
817 * loan of $100,000 at a nominal rate of 13.25% compounded monthly, if
818 * monthly end-of-period payments of $1125.75 are made.
819 *
820 * <>d
821 * <>i=13.25
822 * 13.25
823 * <>pv=100000
824 * 100,000.00
825 * <>pmt=-1125.75
826 * -1,125.75
827 * <>_N(i,pv,pmt,fv,CF,PF,disc,bep)
828 * 360.10
829 * <>N
830 * 360
831 *
832 * Example 5: Final Payment
833 * Using the data in example 4, find the amount of the final payment if n is
834 * changed to 360. The final payment will be equal to the regular payment plus
835 * any balance, future value, remaining at the end of period number 360.
836 * <>n=360
837 * 360.00
838 * <>FV
839 * -108.87
840 * <>pmt+fv
841 * -1,234.62
842 *
843 * Using the data from this loan, compute the amortization schedule
844 * when the Effective date of the loan is June 6, 1996 and the
845 * initial payment is made on August 1, 1996. Ignore any change in
846 * the PV due to the delayed initial payment caused by the partial
847 * payment period from June 6 to July 1.
848 *
849 * <>ED = 06/06/1996
850 * Effective Date set: 06/06/1996 ( 2450241 )
851 * <>IP = 08/01/1996
852 * Initial Payment Date set: 08/01/1996 ( 2450297 )
853 * <>a
854 * Effective Date: 06/06/96
855 * Initial Payment Date: 08/01/96
856 * The amortization options are:
857 * The Old Present Value (pv) was: 100,000.00
858 * The Old Periodic Payment (pmt) was: -1,125.75
859 * The Old Future Value (fv) was: -108.87
860 * 1: Amortize with Original Transaction Values
861 * and balloon final payment: -1,125.75
862 *
863 * The New Present Value (pve) is: 100,919.30
864 * The New Periodic Payment (pmt) is: -1,136.10
865 * 2: Amortize with Original Periodic Payment
866 * and balloon final payment: -49,023.68
867 * 3: Amortize with New Periodic Payment
868 * and balloon final payment: -1,132.57
869 * 4: Amortize with Original Periodic Payment,
870 * new number of total payments (n): 417
871 * and final payment: -2,090.27
872 *
873 * Enter choice 1, 2, 3 or 4: <>
874 *
875 * Press '1'
876 * Amortization Schedule:
877 * Yearly, y, per Payment, p, or Advanced Payment, a, Amortization
878 * Enter choice y, p or a:
879 * <>
880 *
881 * Press 'y'
882 * Enter Filename for Amortization Schedule.
883 * (null string uses Standard Output):
884 * Press enter to display output on screen
885 *
886 * Amortization Table
887 * Effective Date: Thu Jun 06 00:00:00 1996
888 * Initial Payment Date: Thu Aug 01 00:00:00 1996
889 * Compounding Frequency per year: 12
890 * Payment Frequency per year: 12
891 * Compounding: Discrete
892 * Payments: End of Period
893 * Payments (359): -1,125.75
894 * Final payment: -1,125.75
895 * Nominal Annual Interest Rate: 13.25
896 * Effective Interest Rate Per Payment Period: 0.0110417
897 * Present Value: 100,000.00
898 * Year Interest Ending Balance
899 * 1996 -5,518.42 -99,889.67
900 * 1997 -13,218.14 -99,598.81
901 * 1998 -13,177.17 -99,266.98
902 * 1999 -13,130.43 -98,888.41
903 * 2000 -13,077.11 -98,456.52
904 * 2001 -13,016.28 -97,963.80
905 * 2002 -12,946.88 -97,401.68
906 * 2003 -12,867.70 -96,760.38
907 * 2004 -12,777.38 -96,028.76
908 * 2005 -12,674.33 -95,194.09
909 * 2006 -12,556.76 -94,241.85
910 * 2007 -12,422.64 -93,155.49
911 * 2008 -12,269.63 -91,916.12
912 * 2009 -12,095.06 -90,502.18
913 * 2010 -11,895.91 -88,889.09
914 * 2011 -11,668.70 -87,048.79
915 * 2012 -11,409.50 -84,949.29
916 * 2013 -11,113.78 -82,554.07
917 * 2014 -10,776.41 -79,821.48
918 * 2015 -10,391.53 -76,704.01
919 * 2016 -9,952.43 -73,147.44
920 * 2017 -9,451.49 -69,089.93
921 * 2018 -8,879.99 -64,460.92
922 * 2019 -8,227.99 -59,179.91
923 * 2020 -7,484.16 -53,155.07
924 * 2021 -6,635.56 -46,281.63
925 * 2022 -5,667.43 -38,440.06
926 * 2023 -4,562.94 -29,494.00
927 * 2024 -3,302.89 -19,287.89
928 * 2025 -1,865.36 -7,644.25
929 * 2026 -236.00 -108.87
930 *
931 * Total Interest: -305,270.00
932 *
933 * NOTE: The amortization table leaves the FV as it was when the amortization
934 * function was entered. Thus, a balance of 108.87 is due at the end of the
935 * table. To completely pay the loan, set fv to 0.0:
936 * <>fv=0
937 * 0.0
938 * <>a
939 * Effective Date: 06/06/96
940 * Initial Payment Date: 08/01/96
941 * The amortization options are:
942 * The Old Present Value (pv) was: 100,000.00
943 * The Old Periodic Payment (pmt) was: -1,125.75
944 * The Old Future Value (fv) was: 0.00
945 * 1: Amortize with Original Transaction Values
946 * and balloon final payment: -1,234.62
947 *
948 * The New Present Value (pve) is: 100,919.30
949 * The New Periodic Payment (pmt) is: -1,136.12
950 * 2: Amortize with Original Periodic Payment
951 * and balloon final payment: -49,132.55
952 * 3: Amortize with New Periodic Payment
953 * and balloon final payment: -1,148.90
954 * 4: Amortize with Original Periodic Payment,
955 * new number of total payments (n): 417
956 * and final payment: -2,199.14
957 *
958 * Enter choice 1, 2, 3 or 4: <>
959 * Press '1'
960 * Amortization Schedule:
961 * Yearly, y, per Payment, p, or Advanced Payment, a, Amortization
962 * Enter choice y, p or a:
963 * <>
964 * Press 'y'
965 * Enter Filename for Amortization Schedule.
966 * (null string uses Standard Output):
967 * Press enter to display output on screen
968 *
969 * Amortization Table
970 * Effective Date: Thu Jun 06 00:00:00 1996
971 * Initial Payment Date: Thu Aug 01 00:00:00 1996
972 * Compounding Frequency per year: 12
973 * Payment Frequency per year: 12
974 * Compounding: Discrete
975 * Payments: End of Period
976 * Payments (359): -1,125.75
977 * Final payment: -1,234.62
978 * Nominal Annual Interest Rate: 13.25
979 * Effective Interest Rate Per Payment Period: 0.0110417
980 * Present Value: 100,000.00
981 * Year Interest Ending Balance
982 * 1996 -5,518.42 -99,889.67
983 * 1997 -13,218.14 -99,598.81
984 * 1998 -13,177.17 -99,266.98
985 * 1999 -13,130.43 -98,888.41
986 * 2000 -13,077.11 -98,456.52
987 * 2001 -13,016.28 -97,963.80
988 * 2002 -12,946.88 -97,401.68
989 * 2003 -12,867.70 -96,760.38
990 * 2004 -12,777.38 -96,028.76
991 * 2005 -12,674.33 -95,194.09
992 * 2006 -12,556.76 -94,241.85
993 * 2007 -12,422.64 -93,155.49
994 * 2008 -12,269.63 -91,916.12
995 * 2009 -12,095.06 -90,502.18
996 * 2010 -11,895.91 -88,889.09
997 * 2011 -11,668.70 -87,048.79
998 * 2012 -11,409.50 -84,949.29
999 * 2013 -11,113.78 -82,554.07
1000 * 2014 -10,776.41 -79,821.48
1001 * 2015 -10,391.53 -76,704.01
1002 * 2016 -9,952.43 -73,147.44
1003 * 2017 -9,451.49 -69,089.93
1004 * 2018 -8,879.99 -64,460.92
1005 * 2019 -8,227.99 -59,179.91
1006 * 2020 -7,484.16 -53,155.07
1007 * 2021 -6,635.56 -46,281.63
1008 * 2022 -5,667.43 -38,440.06
1009 * 2023 -4,562.94 -29,494.00
1010 * 2024 -3,302.89 -19,287.89
1011 * 2025 -1,865.36 -7,644.25
1012 * 2026 -344.87 0.00
1013 *
1014 * Total Interest: -305,378.87
1015 *
1016 * Example 6: Balloon Payment
1017 * On long term loans, small changes in the periodic payments can generate
1018 * large changes in the future value. If the monthly payment in example 5 is
1019 * rounded down to $1125, how much additional (balloon) payment will be due
1020 * with the final regular payment.
1021 * <>pmt=-1125
1022 * -1,125
1023 * <>FV
1024 * -3,579.99
1025 *
1026 * Example 7: Canadian Mortgage
1027 * Find the monthly end-of-period payment necessary to fully amortize a 25 year
1028 * $85,000 loan at 11% compounded semi-annually.
1029 * <>d
1030 * <>CF=2
1031 * 2.00
1032 * <>n=300
1033 * 300.00
1034 * <>i=11
1035 * 11.00
1036 * <>pv=85000
1037 * 85,000.00
1038 * <>PMT
1039 * -818.15
1040 *
1041 * Example 8: European Mortgage
1042 * The "effective annual rate (EAR)" is used in some countries (especially
1043 * in Europe) in lieu of the nominal rate commonly used in the United States
1044 * and Canada. For a 30 year $90,000 mortgage at 14% (EAR), compute the monthly
1045 * end-of-period payments. When using an EAR, the compounding frequency is
1046 * set to 1.
1047 * <>d
1048 * <>CF=1
1049 * 1.00
1050 * <>n=30*12
1051 * 360.00
1052 * <>i=14
1053 * 14.00
1054 * <>pv=90000
1055 * 90,000.00
1056 * <>PMT
1057 * -1,007.88
1058 *
1059 * Example 9: Bi-weekly Savings
1060 * Compute the future value, fv, of bi-weekly savings of $100 for 3 years at a
1061 * nominal annual rate of 5.5% compounded daily. (Set payment to
1062 * beginning-of-period, bep = TRUE)
1063 * <>d
1064 * <>bep=TRUE
1065 * 1.00
1066 * <>CF=365
1067 * 365.00
1068 * <>PF=26
1069 * 26.00
1070 * <>n=3*26
1071 * 78.00
1072 * <>i=5.5
1073 * 5.50
1074 * <>pmt=-100
1075 * -100.00
1076 * <>FV
1077 * 8,489.32
1078 *
1079 * Example 10: Present Value - Annuity Due
1080 * What is the present value of $500 to be received at the beginning of each
1081 * quarter over a 10 year period if money is being discounted at 10% nominal
1082 * annual rate compounded monthly?
1083 * <>d
1084 * <>bep=TRUE
1085 * 1.00
1086 * <>PF=4
1087 * 4.00
1088 * <>n=4*10
1089 * 40.00
1090 * <>i=10
1091 * 10.00
1092 * <>pmt=500
1093 * 500.00
1094 * <>PV
1095 * -12,822.64
1096 *
1097 * Example 11: Effective Rate - 365/360 Basis
1098 * Compute the effective annual rate (%APR) for a nominal annual rate of 12%
1099 * compounded on a 365/360 basis used by some Savings & Loan Associations.
1100 * <>d
1101 * <>n=365
1102 * 365.00
1103 * <>CF=365
1104 * 365.00
1105 * <>PF=360
1106 * 360.00
1107 * <>i=12
1108 * 12.00
1109 * <>pv=-100
1110 * -100.00
1111 * <>FV
1112 * 112.94
1113 * <>fv+pv
1114 * 12.94
1115 *
1116 * Example 12: Mortgage with "Points"
1117 *
1118 * What is the true APR of a 30 year, $75,000 loan at a nominal rate
1119 * of 13.25% compounded monthly, with monthly end-of-period payments,
1120 * if 3 "points" are charged? The pv must be reduced by the dollar
1121 * value of the points and/or any lenders fees to establish an
1122 * effective pv. Because payments remain the same, the true APR will
1123 * be higher than the nominal rate. Note, first compute the payments
1124 * on the pv of the loan amount.
1125 *
1126 * <>d
1127 * <>CF=PF=1
1128 * 1.00
1129 * <>n=30*12
1130 * 360.00
1131 * <>i=13.25/12
1132 * 1.10
1133 * <>pv=75000
1134 * 75,000.00
1135 * <>PMT
1136 * -844.33
1137 * <>pv -= pv*.03
1138 * 72,750.00
1139 * <>CF=PF=12
1140 * 12.00
1141 * <>I
1142 * 13.69
1143 *
1144 * Example 13: Equivalent Payments
1145 * Find the equivalent monthly payment required to amortize a 20 year $40,000
1146 * loan at 10.5% nominal annual rate compounded monthly, with 10 annual
1147 * payments of $5029.71 remaining. Compute the pv of the remaining annual
1148 * payments, then change n, the number of periods, and the payment frequency,
1149 * PF, to a monthly basis and compute the equivalent monthly pmt.
1150 * <>d
1151 * <>PF=1
1152 * 1.00
1153 * <>n=10
1154 * 10.00
1155 * <>i=10.5
1156 * 10.50
1157 * <>pmt=-5029.71
1158 * -5,029.71
1159 * <>PV
1160 * 29,595.88
1161 * <>PF=12
1162 * 12.00
1163 * <>n=120
1164 * 120.00
1165 * <>PMT
1166 * -399.35
1167 *
1168 * Example 14: Perpetuity - Continuous Compounding
1169 * If you can purchase a single payment annuity with an initial investment of
1170 * $60,000 that will be invested at 15% nominal annual rate compounded
1171 * continuously, what is the maximum monthly return you can receive without
1172 * reducing the $60,000 principal? If the principal is not disturbed, the
1173 * payments can go on indefinitely (a perpetuity). Note that the term,n, of
1174 * a perpetuity is immaterial. It can be any non-zero value.
1175 * <>d
1176 * <>disc=FALSE
1177 * 0.00
1178 * <>n=12
1179 * 12.00
1180 * <>CF=1
1181 * 1.00
1182 * <>i=15
1183 * 15.00
1184 * <>fv=60000
1185 * 60,000.00
1186 * <>pv=-60000
1187 * -60,000.00
1188 * <>PMT
1189 * 754.71
1190 *
1191 * references:
1192 * 1. PPC ROM User's Manual
1193 * pages 148 - 164
1194 *
1195 */
1196
1197#include <time.h>
1198#include <stdio.h>
1199#include <glib.h>
1200#include <math.h>
1201#if defined(G_OS_WIN32) && !defined(_MSC_VER)
1202#include <pow.h>
1203#endif
1204#include <string.h>
1205#include <stdlib.h>
1206
1207#define FIN_STATICS
1208#include "finvar.h"
1209#include "finproto.h"
1210#include "fin_static_proto.h"
1211
1212/* return 'x' rounded to 'places' past decimal if 'places' < 0, return
1213 * 'x' */
1214static double
1215rnd (double x, unsigned places)
1216{
1217 static const size_t buflen = 50; /* make buffer large enough */
1218 double r;
1219 char buf[buflen];
1220
1221 snprintf (buf, buflen, "%.*f", (int) places, x);
1222 r = strtod(buf, NULL);
1223
1224 return r;
1225} /* rnd */
1226
1227/* return absolute value of 'x' this function is provided by a macro
1228 * in C */
1229static double
1230dabs (double x)
1231{
1232 return (x >= 0.0) ? x : -x;
1233} /* dabs */
1234
1235/* Compute constant used in calculations */
1236static double
1237_A (double eint, unsigned per)
1238{
1239 return pow ((1.0 + eint), (double) per) - 1.0;
1240} /* _A */
1241
1242/* Compute constant used in calculations */
1243static double
1244_B (double eint, unsigned beg)
1245{
1246 /* if eint == 0.0, all processing _must_ stop or
1247 a recursive loop will start. */
1248 g_return_val_if_fail(eint != 0.0, 0.0);
1249 return (1.0 + eint * (double) beg) / eint;
1250} /* _B */
1251
1252/* Compute constant used in calculations */
1253static double
1254_C (double eint, double pmt, unsigned beg)
1255{
1256 g_return_val_if_fail(eint != 0.0, 0.0);
1257 return pmt * _B(eint, beg);
1258} /* _C */
1259
1260/* compute Number of Periods from preset data */
1261unsigned
1262fi_calc_num_payments (fi_ptr fi)
1263{
1264 return fi->npp =
1265 (unsigned)
1266 rnd (_fi_calc_num_payments
1267 (fi->ir, fi->pv, fi->pmt, fi->fv, fi->CF, fi->PF, fi->disc, fi->bep),
1268 0);
1269} /* fi_calc_num_payments */
1270
1271/* Compute number of periods from:
1272 * 1. Nominal Interest
1273 * 2. Present Value
1274 * 3. Periodic Payment
1275 * 4. Future Value
1276 */
1277double
1278_fi_calc_num_payments (double nint, /* nominal interest rate */
1279 double pv, /* present value */
1280 double pmt, /* periodic payment */
1281 double fv, /* future value */
1282 unsigned CF, /* compounding frequency */
1283 unsigned PF, /* payment frequency */
1284 unsigned disc, /* discrete/continuous compounding */
1285 unsigned bep) /* beginning/end of period payment */
1286{
1287 double eint = eff_int (nint / 100.0, CF, PF, disc);
1288 double CC = _C (eint, pmt, bep);
1289 CC = (CC - fv) / (CC + pv);
1290 return (CC > 0.0) ? log (CC) / log (1.0 + eint) : 0.0;
1291} /* _fi_calc_num_payments */
1292
1293/* compute Interest from preset data */
1294double
1295fi_calc_interest (fi_ptr fi)
1296{
1297 if (fi->npp)
1298 fi->ir = _fi_calc_interest (fi->npp, fi->pv, fi->pmt, fi->fv,
1299 fi->CF, fi->PF, fi->disc, fi->bep);
1300
1301 return fi->ir;
1302} /* fi_calc_interest */
1303
1304double ratio = 1e4; /* ratio used in iterative solution for interest */
1305
1306/* Compute Nominal Interest from:
1307 * 1. Number of periods
1308 * 2. Present Value
1309 * 3. Periodic Payment
1310 * 4. Future Value
1311 */
1312double
1313_fi_calc_interest (unsigned per,/* number of periods */
1314 double pv, /* present value */
1315 double pmt, /* periodic payment */
1316 double fv, /* future value */
1317 unsigned CF, /* compounding frequency */
1318 unsigned PF, /* payment frequency */
1319 unsigned disc, /* discrete/continuous compounding */
1320 unsigned bep) /* beginning/end of period payment */
1321{
1322 double eint;
1323 double a, dik;
1324 int ri;
1325
1326 if (pmt == 0.0)
1327 eint = pow ((dabs (fv) / dabs (pv)), (1.0 / (double) per)) - 1.0;
1328 else
1329 {
1330 if ((pmt * fv) < 0.0)
1331 {
1332 if (pv)
1333 a = -1.0;
1334 else
1335 a = 1.0;
1336 eint =
1337 dabs ((fv + a * (double) per * pmt) /
1338 (3.0 *
1339 (((double) per - 1.0) * ((double) per - 1.0) * pmt + pv -
1340 fv)));
1341 }
1342 else
1343 {
1344 if ((pv * pmt) < 0.0)
1345 {
1346 eint = dabs (((double) per * pmt + pv + fv) / ((double) per * pv));
1347 }
1348 else
1349 {
1350 a = dabs (pmt / (dabs (pv) + dabs (fv)));
1351 eint = a + 1.0 / (a * (double) per * (double) per * (double) per);
1352 }
1353 }
1354 do
1355 {
1356 dik =
1357 fi (per, eint, pv, pmt, fv, bep) / fip (per, eint, pv, pmt, fv, bep);
1358 eint -= dik;
1359 (void) modf (ratio * (dik / eint), &a);
1360 ri = (unsigned) a;
1361 }
1362 while (ri);
1363 } /* endif */
1364
1365 return 100.0 * nom_int (eint, CF, PF, disc);
1366} /* _fi_calc_interest */
1367
1368/* compute Present value from preset data */
1369double
1370fi_calc_present_value (fi_ptr fi)
1371{
1372 return fi->pv =
1373 rnd (_fi_calc_present_value
1374 (fi->npp, fi->ir, fi->pmt, fi->fv, fi->CF, fi->PF, fi->disc,
1375 fi->bep), fi->prec);
1376} /* fi_calc_present_value */
1377
1378/* Compute Present Value from:
1379 * 1. Number of periods
1380 * 2. Nominal Interest
1381 * 3. Periodic Payment
1382 * 4. Future Value
1383 */
1384double
1385_fi_calc_present_value (unsigned per, /* number of periods */
1386 double nint, /* nominal interest rate */
1387 double pmt, /* periodic payment */
1388 double fv, /* future value */
1389 unsigned CF, /* compounding frequency */
1390 unsigned PF, /* payment frequency */
1391 unsigned disc, /* discrete/continuous compounding */
1392 unsigned bep) /* beginning/end of period payment */
1393{
1394 double eint = eff_int (nint / 100.0, CF, PF, disc);
1395 double AA = _A (eint, per);
1396 double CC = _C (eint, pmt, bep);
1397
1398 return -(fv + (AA * CC)) / (AA + 1.0);
1399} /* _fi_calc_present_value */
1400
1401/* compute Periodic Payment from preset data */
1402double
1403fi_calc_payment (fi_ptr fi)
1404{
1405 return fi->pmt =
1406 rnd (_fi_calc_payment
1407 (fi->npp, fi->ir, fi->pv, fi->fv, fi->CF, fi->PF, fi->disc, fi->bep),
1408 fi->prec);
1409} /* fi_calc_payment */
1410
1411/* Compute Periodic Payment from:
1412 * 1. Number of periods
1413 * 2. Nominal Interest
1414 * 3. Present Value
1415 * 4. Future Value
1416 */
1417double
1418_fi_calc_payment (unsigned per, /* number of periods */
1419 double nint, /* nominal interest rate */
1420 double pv, /* present value */
1421 double fv, /* future value */
1422 unsigned CF, /* compounding frequency */
1423 unsigned PF, /* payment frequency */
1424 unsigned disc,/* discrete/continuous compounding */
1425 unsigned bep) /* beginning/end of period payment */
1426{
1427 double eint = eff_int (nint / 100.0, CF, PF, disc);
1428 double AA = _A (eint, per);
1429 double BB = _B (eint, bep);
1430 g_return_val_if_fail(BB != 0.0, 0.0);
1431
1432 return -(fv + pv * (AA + 1.0)) / (AA * BB);
1433} /* _fi_calc_payment */
1434
1435/* compute Future Value from preset data */
1436double
1437fi_calc_future_value (fi_ptr fi)
1438{
1439 return fi->fv =
1440 rnd (_fi_calc_future_value
1441 (fi->npp, fi->ir, fi->pv, fi->pmt, fi->CF, fi->PF, fi->disc,
1442 fi->bep), fi->prec);
1443} /* fi_calc_future_value */
1444
1445/* Compute Future Value from:
1446 * 1. Number of periods
1447 * 2. Nominal Interest
1448 * 3. Present Value
1449 * 4. Periodic Payments
1450 */
1451double
1452_fi_calc_future_value (unsigned per, /* number of periods */
1453 double nint, /* nominal interest rate */
1454 double pv, /* present value */
1455 double pmt, /* periodic payment */
1456 unsigned CF, /* compounding frequency */
1457 unsigned PF, /* payment frequency */
1458 unsigned disc, /* discrete/continuous compounding */
1459 unsigned bep) /* beginning/end of period payment */
1460{
1461 double eint = eff_int (nint / 100.0, CF, PF, disc);
1462 double AA = _A (eint, per);
1463 double CC = _C (eint, pmt, bep);
1464
1465 return -(pv + AA * (pv + CC));
1466} /* _fi_calc_future_value */
1467
1468/* compute Nominal Interest Rate from Effective Interest Rate */
1469static double
1470nom_int (double eint, unsigned CF, unsigned PF, unsigned disc)
1471{
1472 double nint;
1473
1474 if (disc)
1475 {
1476 if (CF == PF)
1477 {
1478 nint = CF * eint;
1479 }
1480 else
1481 {
1482 nint = CF * (pow ((1.0 + eint), ((double) PF / (double) CF)) - 1.0);
1483 } /* * endif */
1484 }
1485 else
1486 nint = log (pow (1.0 + eint, PF));
1487
1488 return nint;
1489} /* nom_int */
1490
1491/* Compute Effective Interest Rate from Nominal Interest Rate */
1492static double
1493eff_int (double nint, unsigned CF, unsigned PF, unsigned disc)
1494{
1495 double eint;
1496
1497 if (disc)
1498 {
1499 if (CF == PF)
1500 {
1501 eint = nint / (double) CF;
1502 }
1503 else
1504 {
1505 eint =
1506 pow ((1.0 + nint / (double) CF), ((double) CF / (double) PF)) - 1.0;
1507 } /* endif */
1508 }
1509 else
1510 eint = exp (nint / (double) PF) - 1.0;
1511
1512 return eint;
1513} /* eff_int */
1514
1515/* calculation used in interest computation */
1516static double
1517fi (unsigned per, double eint, double pv, double pmt, double fv, unsigned bep)
1518{
1519 return _A (eint, per) * (pv + _C (eint, pmt, bep)) + pv + fv;
1520} /* fi */
1521
1522/* calculation used in interest computation
1523 */
1524static double
1525fip (unsigned per, double eint, double pv, double pmt, double fv, unsigned bep)
1526{
1527 double AA = _A (eint, per);
1528 double CC = _C (eint, pmt, bep);
1529 double D = (AA + 1.0) / (1.0 + eint);
1530 g_return_val_if_fail(CC != 0.0, 0.0);
1531 return (double) per * (pv + CC) * D - (AA * CC) / eint;
1532} /* fip */
1533
1534void
1535set_default (fi_ptr fi)
1536{
1537 /* flag whether accrueing interest at beginning or end of period
1538 * FALSE --> end
1539 * TRUE --> beginning
1540 * default to end of period payment s
1541 */
1542 fi->bep = FALSE;
1543
1544 /* flag for discrete or continuous interest
1545 * TRUE --> discrete
1546 * FALSE --> continuous
1547 * default to discrete interest
1548 */
1549 fi->disc = TRUE;
1550
1551 /* set compounding, CF, and payment, PF, frequency per year
1552 * default to monthly payments and compounding
1553 */
1554 fi->CF = fi->PF = 12;
1555
1556 /* standard loan quantities:
1557 * number of periods: n
1558 */
1559 fi->npp = 0;
1560
1561 /* annual interest: i
1562 */
1563 fi->ir = 0.0;
1564
1565 /* Present Value: pv
1566 */
1567 fi->pv = 0.0;
1568
1569 /* Payment: pmt
1570 */
1571 fi->pmt = 0.0;
1572
1573 /* Future Value: fv
1574 */
1575 fi->fv = 0.0;
1576
1577} /* set_default */
1578
1579/* compute Julian Day Number from calendar date
1580 */
1581unsigned long
1582julian_day_number (unsigned year, unsigned month, unsigned day)
1583{
1584 /* Gregorian/Julian Calendar Flag.
1585 * TRUE == Julian
1586 * FALSE == Gregorian
1587 */
1588 unsigned gregorian = TRUE; /* assume we are dealing with current dates */
1589 double yr;
1590 double pfac = 0.6;
1591 unsigned long ljdn;
1592
1593 yr = year + (month - 3.0) / 12.0;
1594 ljdn = (long) (367.0 * yr + pfac) - (2 * (long) (yr)) + (long) (yr / 4.0)
1595 + (long) day + 1721117L;
1596 if (gregorian)
1597 ljdn += -(long) (yr / 100.0) + (long) (yr / 400.0) + 2;
1598
1599 return ljdn;
1600} /* julian_day_number */
1601
1602amort_sched_ptr
1603Amortization_init (amort_sched_ptr amortsched)
1604{
1605 unsigned n = amortsched->n;
1606 double nint = amortsched->nint;
1607 double pv = amortsched->pv;
1608 double pmt = amortsched->pmt;
1609 double fv = amortsched->fv;
1610 double eint;
1611 double new_pmt;
1612 double pve;
1613 unsigned CF = amortsched->CF;
1614 unsigned PF = amortsched->PF;
1615 unsigned disc = amortsched->disc;
1616 unsigned bep = amortsched->bep;
1617 unsigned new_n;
1618 unsigned prec = amortsched->prec;
1619 unsigned long s,
1620 d,
1621 days_to_yr_end,
1622 Eff_Date_jdn =
1623 julian_day_number (amortsched->year_E, amortsched->month_E,
1624 amortsched->day_E), Init_Date_jdn =
1625 julian_day_number (amortsched->year_I, amortsched->month_I,
1626 amortsched->day_I);
1627
1628 amortsched->Eff_Date_jdn = Eff_Date_jdn;
1629 amortsched->Init_Date_jdn = Init_Date_jdn;
1630 amortsched->yday_E =
1631 Eff_Date_jdn - julian_day_number (amortsched->year_E, 1, 1);
1632 amortsched->yday_I =
1633 Init_Date_jdn - julian_day_number (amortsched->year_I, 1, 1);
1634 amortsched->eint = eint = eff_int (nint / 100.0, CF, PF, disc);
1635 amortsched->fv_case = dabs (fv) > dabs (pv);
1636 amortsched->bp = bep ? 1.0 : 0.0;
1637
1638 if (PF > 24)
1639 {
1640 /* Payment frequency per year greater than bi-monthly
1641 * use actual number of days
1642 */
1643 s = Init_Date_jdn - Eff_Date_jdn;
1644 days_to_yr_end =
1645 julian_day_number (amortsched->year_I + 1, 1, 0) - Init_Date_jdn;
1646 d = 366 / PF;
1647 }
1648 else
1649 {
1650 /* Payment frequency per year bi-monthly or less
1651 * use 30 days/month, 360 days/year
1652 */
1653 if (Eff_Date_jdn == Init_Date_jdn)
1654 {
1655 s = 0;
1656 }
1657 else
1658 {
1659 s =
1660 ((amortsched->year_I - amortsched->year_E) * 360) +
1661 ((amortsched->month_I - amortsched->month_E) * 30) +
1662 amortsched->day_I - amortsched->day_E;
1663 } /* endif */
1664 days_to_yr_end = 390 - (amortsched->month_I * 30) - amortsched->day_I;
1665 d = 360 / PF;
1666 } /* endif */
1667
1668 if (!bep)
1669 {
1670 /* ordinary annuity
1671 */
1672 s -= d;
1673 } /* endif */
1674
1675 amortsched->yr_pmt = (days_to_yr_end + d) / d;
1676
1677 if (pmt == 0.0)
1678 {
1679 amortsched->pve = pv;
1680 }
1681 else
1682 {
1683 amortsched->pve =
1684 rnd (pv * pow ((1.0 + eint), ((double) (s * PF) / (double) (d * CF))),
1685 prec);
1686 } /* endif */
1687
1688 pve = amortsched->pve;
1689
1690 /* compute new data to fully amortize loan:
1691 * new periodic payment, new_pmt
1692 *
1693 * option 1: Amortize with original transaction - ignore interest
1694 * due to delayed initial payment
1695 *
1696 * option 2: Amortize with new pv, pve == original pv adjusted for
1697 * delayed initial payment, original payment, original fv and
1698 * original total number of payments, adjust final payment
1699 *
1700 * option 3: amortize with new pv, pve, and new payments adjusted to
1701 * minimize final payment, keep original number of payments and
1702 * original fv
1703 *
1704 * option 4: amortize with new pv, pve, original payments and new
1705 * number of payments to keep original final fv */
1706
1707 /* option 3, compute new periodic payment */
1708 amortsched->new_pmt = new_pmt =
1709 rnd (_fi_calc_payment (n, nint, pve, fv, CF, PF, disc, bep), prec);
1710
1711 /* option 4: compute new number of total payments, new_n */
1712 amortsched->new_n = new_n =
1713 (unsigned)
1714 rnd (_fi_calc_num_payments (nint, pve, pmt, fv, CF, PF, disc, bep), 0);
1715
1716 /* following used in QTAwk to insure integer value, not needed in C */
1717 /* n = int(n); */
1718
1719 /* compute payment for constant payment to principal loan and final
1720 * payment for original loan amount include interest due */
1721 amortsched->cpmt1 = rnd (-pv / n, prec);
1722 amortsched->final_pmt_opt_1 = -pv - amortsched->cpmt1 * (n - 1);
1723 amortsched->final_pmt_opt_1 *= eint + 1;
1724
1725 /* compute payment for constant payment to principal loan and final
1726 * payment for delayed loan amount include interest due */
1727 amortsched->cpmt2 = rnd (-pve / n, prec);
1728 amortsched->final_pmt_opt_2 = -pve - amortsched->cpmt2 * (n - 1);
1729 amortsched->final_pmt_opt_2 *= eint + 1;
1730
1731 if (bep)
1732 {
1733 amortsched->final_pmt_opt_3 =
1734 rnd (_fi_calc_future_value (n - 1, nint, pv, pmt, CF, PF, disc, bep) -
1735 (fv / (1.0 + eint)), prec);
1736 amortsched->final_pmt_opt_4 =
1737 rnd (_fi_calc_future_value (n - 1, nint, pve, pmt, CF, PF, disc, bep) -
1738 (fv / (1.0 + eint)), prec);
1739 amortsched->final_pmt_opt_5 =
1740 rnd (_fi_calc_future_value
1741 (n - 1, nint, pve, new_pmt, CF, PF, disc,
1742 bep) - (fv / (1.0 + eint)), prec);
1743 if (new_n)
1744 amortsched->final_pmt_opt_6 =
1745 rnd (_fi_calc_future_value
1746 (new_n - 1, nint, pve, pmt, CF, PF, disc,
1747 bep) - (fv / (1.0 + eint)), prec);
1748 else
1749 amortsched->final_pmt_opt_6 = 0.0;
1750 }
1751 else
1752 {
1753 amortsched->final_pmt_opt_3 =
1754 rnd (_fi_calc_future_value (n - 1, nint, pv, pmt, CF, PF, disc, bep) *
1755 (1.0 + eint) - fv, prec);
1756 amortsched->final_pmt_opt_4 =
1757 rnd (_fi_calc_future_value (n - 1, nint, pve, pmt, CF, PF, disc, bep) *
1758 (1.0 + eint) - fv, prec);
1759 amortsched->final_pmt_opt_5 =
1760 rnd (_fi_calc_future_value
1761 (n - 1, nint, pve, new_pmt, CF, PF, disc, bep) * (1.0 + eint) - fv,
1762 prec);
1763 if (new_n)
1764 amortsched->final_pmt_opt_6 =
1765 rnd (_fi_calc_future_value
1766 (new_n - 1, nint, pve, pmt, CF, PF, disc,
1767 bep) * (1.0 + eint) - fv, prec);
1768 else
1769 amortsched->final_pmt_opt_6 = 0.0;
1770 } /* endif */
1771
1772 /* compute delayed interest */
1773 amortsched->delayed_int = pv - amortsched->pve;
1774
1775 return amortsched;
1776} /* Amortization_init */
1777
1778amort_sched_ptr
1779Amortization_Schedule (amort_sched_ptr amortsched)
1780{
1781 unsigned n = amortsched->n;
1782 double nint = amortsched->nint;
1783 double pv = amortsched->pv;
1784 double pmt = amortsched->pmt;
1785 double fv = amortsched->fv;
1786 double eint = amortsched->eint;
1787 unsigned CF = amortsched->CF;
1788 unsigned PF = amortsched->PF;
1789 unsigned disc = amortsched->disc;
1790 unsigned bep = amortsched->bep;
1791 double cpmt = 0;
1792 double final_pmt = 0;
1793 char summary = amortsched->summary;
1794 unsigned option = amortsched->option;
1795 unsigned yr_pmt = amortsched->yr_pmt;
1796 unsigned fv_case = amortsched->fv_case;
1797 unsigned prec = amortsched->prec;
1798 unsigned j, s, yr, per_cnt, pmt_cnt = 0, k = 0, sum_prt;
1799
1800 int jj;
1801
1802 unsigned long d;
1803
1804 double yr_fv, sum_int, yr_int, prin, adv_pmt, pmt_int, hpv = 0.0;
1805 yearly_summary_ptr yrly_sum;
1806 amort_sched_yr_ptr amortyr;
1807 sched_pmt_ptr pmtsched = NULL;
1808
1809 sum_int = yr_int = 0.0;
1810
1811 switch (option)
1812 {
1813 case 1:
1814 amortsched->cpmt = cpmt = amortsched->cpmt1;
1815 /* re-compute final payment without interest
1816 */
1817 amortsched->final_pmt = final_pmt = -pv - cpmt * (n - 1);
1818 summary = (summary == 'y') ? 'x' : 'o';
1819 break;
1820 case 2:
1821 amortsched->cpmt = cpmt = amortsched->cpmt2;
1822 pv = amortsched->pve;
1823 /* re-compute final payment without interest
1824 */
1825 amortsched->final_pmt = final_pmt = -pv - cpmt * (n - 1);
1826 summary = (summary == 'y') ? 'x' : 'o';
1827 break;
1828 case 3:
1829 amortsched->final_pmt = final_pmt = amortsched->final_pmt_opt_3;
1830 break;
1831 case 4:
1832 pv = amortsched->pve;
1833 amortsched->final_pmt = final_pmt = amortsched->final_pmt_opt_4;
1834 break;
1835 case 5:
1836 pv = amortsched->pve;
1837 pmt = amortsched->new_pmt;
1838 amortsched->final_pmt = final_pmt = amortsched->final_pmt_opt_5;
1839 break;
1840 case 6:
1841 n = amortsched->new_n;
1842 pv = amortsched->pve;
1843 amortsched->final_pmt = final_pmt = amortsched->final_pmt_opt_6;
1844 break;
1845 } /* endswitch */
1846
1847 yr = amortsched->year_I;
1848 sum_prt = TRUE;
1849 switch (summary)
1850 {
1851 case 'a':
1852 /* variable advanced prepayment schedule. prepayment equals next
1853 * period principal. */
1854 amortsched->schedule.first_yr =
1855 amortyr = (amort_sched_yr_ptr) calloc (1, sizeof (amort_sched_yr));
1856
1857 for (per_cnt = 0, s = 1, j = n; pv != fv; j -= 2, per_cnt++)
1858 {
1859 /* basic equation to compute interest this payment period */
1860 pmt_int = -rnd ((pv + (amortsched->bp * pmt)) * eint, prec);
1861
1862 /* sum yearly interest paid */
1863 yr_int += pmt_int;
1864
1865 /* sum total interest paid */
1866 sum_int += pmt_int;
1867
1868 /* compute principal paid this payment period and round to
1869 nearest cent */
1870 if (dabs (pmt) > dabs (pv))
1871 {
1872 prin = -pv;
1873 pmt = prin + pmt_int;
1874 adv_pmt = 0.0;
1875 pv = fv;
1876 }
1877 else
1878 {
1879 prin = rnd (pmt - pmt_int, prec);
1880
1881 /* compute remaining pv and round to nearest cent */
1882 pv = rnd (pv + prin, prec);
1883
1884 /* compute principal for next payment cycle and round to
1885 nearest cent */
1886 adv_pmt = rnd (pmt + (pv + (amortsched->bp * pmt)) * eint, prec);
1887
1888 if (dabs (pv) >= dabs (adv_pmt))
1889 {
1890 /* remaining pv greater than advanced principal payment
1891 * compute remaining pv and round to nearest cent */
1892 pv = rnd (pv + adv_pmt, prec);
1893 }
1894 else
1895 {
1896 /* remaining pv less than advanced principal payment reduce
1897 * advanced pricipla payment to remaining pv */
1898 adv_pmt = -pv;
1899
1900 /* and set remaining pv to fv */
1901 pv = fv;
1902 } /* ## endif */
1903 } /* # endif */
1904
1905 if (sum_prt)
1906 {
1907 jj = (j < yr_pmt) ? j + 1 : yr_pmt;
1908 amortyr->payments =
1909 pmtsched = (sched_pmt_ptr) calloc (jj, sizeof (sched_pmt));
1910 pmt_cnt = 0;
1911
1912 sum_prt = FALSE;
1913 } /* endif */
1914
1915 pmtsched->period_num = s++;
1916 pmtsched->interest = pmt_int;
1917 pmtsched->principal = prin;
1918 pmtsched->advanced_pmt = adv_pmt;
1919 pmtsched->total_pmt = pmt + adv_pmt;
1920 pmtsched->balance = pv;
1921 pmtsched++;
1922 pmt_cnt++;
1923
1924 if (!--yr_pmt)
1925 {
1926 yr_pmt = PF;
1927
1928 amortyr->year = yr++;
1929 amortyr->interest_pd = yr_int;
1930 amortyr->principal_pd = pv - hpv;
1931 amortyr->yr_end_balance = pv;
1932 amortyr->total_interest_pd = sum_int;
1933 amortyr->num_periods = pmt_cnt;
1934 amortyr->next_yr =
1935 (amort_sched_yr_ptr) calloc (1, sizeof (amort_sched_yr));
1936 amortyr = amortyr->next_yr;
1937
1938 hpv = pv;
1939 yr_int = 0.0;
1940 sum_prt = TRUE;
1941 } /* endif */
1942 } /* endfor */
1943
1944 if (dabs (pv) > 0.0)
1945 {
1946 /* basic equation to compute interest this payment period */
1947 pmt_int = -rnd ((pv + (amortsched->bp * pmt)) * eint, prec);
1948
1949 /* sum yearly interest paid */
1950 yr_int += pmt_int;
1951
1952 /* sum total interest paid */
1953 sum_int += pmt_int;
1954
1955 /* compute principal paid this payment period and round to
1956 nearest cent */
1957 prin = rnd (pmt - pmt_int, prec);
1958 final_pmt = pmt;
1959
1960 /* compute remaining pv and round to nearest cent */
1961 pv = rnd (pv + prin, prec);
1962
1963 /* Set advanced principal payment to remaining pv */
1964 adv_pmt = -pv;
1965 amortyr->final_pmt = final_pmt += adv_pmt;
1966
1967 /* and set remaining pv to fv */
1968 pv = fv;
1969
1970 if (pmtsched)
1971 {
1972 pmtsched->period_num = s++;
1973 pmtsched->interest = pmt_int;
1974 pmtsched->principal = prin;
1975 pmtsched->advanced_pmt = adv_pmt;
1976 pmtsched->total_pmt = final_pmt;
1977 pmtsched->balance = pv;
1978 }
1979
1980 per_cnt++;
1981 pmt_cnt++;
1982 } /* endif */
1983
1984 if (dabs (yr_int) > 0.0)
1985 {
1986 amortyr->year = yr++;
1987 amortyr->interest_pd = yr_int;
1988 amortyr->principal_pd = pv - hpv;
1989 amortyr->total_interest_pd = sum_int;
1990 amortyr->num_periods = pmt_cnt;
1991 } /* endif */
1992
1993 amortsched->total_periods = per_cnt;
1994 break;
1995 case 'f':
1996 /* fixed prepaymet schedule prepayment specified by user */
1997 amortsched->schedule.first_yr =
1998 amortyr = (amort_sched_yr_ptr) calloc (1, sizeof (amort_sched_yr));
1999
2000 /* set advnaced payment */
2001 adv_pmt = amortsched->fixed_pmt;
2002
2003 for (per_cnt = 0, s = 1, j = n; j && (pv != fv); j--, per_cnt++)
2004 {
2005 /* basic equation to compute interest this payment period */
2006 pmt_int = -rnd ((pv + (amortsched->bp * pmt)) * eint, prec);
2007 /* sum yearly interest paid
2008 */
2009 yr_int += pmt_int;
2010 /* sum total interest paid */
2011 sum_int += pmt_int;
2012
2013 /* compute principal paid this payment period and round to
2014 nearest cent */
2015 if (dabs (pmt) > dabs (pv))
2016 {
2017 prin = -pv;
2018 pmt = prin + pmt_int;
2019 adv_pmt = 0.0;
2020 pv = 0.0;
2021 }
2022 else
2023 {
2024 prin = rnd (pmt - pmt_int, prec);
2025
2026 /* compute remaining pv and round to nearest cent */
2027 pv = rnd (pv + prin, prec);
2028
2029 if (dabs (pv) >= dabs (adv_pmt))
2030 {
2031 /* remaining pv greater than advanced principal payment
2032 * compute remaining pv and round to nearest cent */
2033 pv = rnd (pv + adv_pmt, prec);
2034 }
2035 else
2036 {
2037 /* remaining pv less than advanced principal payment reduce
2038 * advanced principal payment to remaining pv and set
2039 * remaining pv to fv */
2040 adv_pmt = -pv;
2041 pv = fv;
2042 } /*## endif */
2043 } /* # endif */
2044
2045 if (sum_prt)
2046 {
2047 jj = (j < yr_pmt) ? j + 1 : yr_pmt;
2048 amortyr->payments =
2049 pmtsched = (sched_pmt_ptr) calloc (jj, sizeof (sched_pmt));
2050 pmt_cnt = 0;
2051
2052 sum_prt = FALSE;
2053 }
2054 else
2055 {
2056 (amortyr->num_periods)++;
2057 } /* ## endif */
2058
2059 pmtsched->period_num = s++;
2060 pmtsched->interest = pmt_int;
2061 pmtsched->principal = prin;
2062 pmtsched->advanced_pmt = adv_pmt;
2063 pmtsched->total_pmt = pmt + adv_pmt;
2064 pmtsched->balance = pv;
2065 pmt_cnt++;
2066 pmtsched++;
2067
2068 if (!--yr_pmt)
2069 {
2070 yr_pmt = PF;
2071
2072 amortyr->year = yr++;
2073 amortyr->interest_pd = yr_int;
2074 amortyr->principal_pd = pv - hpv;
2075 amortyr->yr_end_balance = pv;
2076 amortyr->total_interest_pd = sum_int;
2077 amortyr->num_periods = pmt_cnt;
2078 amortyr->next_yr =
2079 (amort_sched_yr_ptr) calloc (1, sizeof (amort_sched_yr));
2080 amortyr = amortyr->next_yr;
2081
2082 hpv = pv;
2083 yr_int = 0.0;
2084 sum_prt = TRUE;
2085 } /* ## endif */
2086 } /* ## endfor */
2087
2088 if (pv != fv)
2089 {
2090 /* # basic equation to compute interest this payment period */
2091 pmt_int = -rnd ((pv + (amortsched->bp * pmt)) * eint, prec);
2092
2093 /* # sum yearly interest paid */
2094 yr_int += pmt_int;
2095 /* # sum total interest paid */
2096 sum_int += pmt_int;
2097
2098 /* # compute principal paid this payment period and round to
2099 nearest cent */
2100 prin = rnd (pmt - pmt_int, prec);
2101 final_pmt = pmt;
2102
2103 /* # compute remaining pv and round to nearest cent */
2104 pv = rnd (pv + prin, prec);
2105
2106 /* # Set advanced principal payment to remaining pv */
2107 adv_pmt = -pv;
2108 amortyr->final_pmt = final_pmt += adv_pmt;
2109
2110 /* # and set remaining pv to fv */
2111 pv = fv;
2112
2113 if (pmtsched)
2114 {
2115 pmtsched->period_num = s++;
2116 pmtsched->interest = pmt_int;
2117 pmtsched->principal = prin;
2118 pmtsched->advanced_pmt = adv_pmt;
2119 pmtsched->total_pmt = final_pmt;
2120 pmtsched->balance = pv;
2121 }
2122
2123 per_cnt++;
2124 pmt_cnt++;
2125 } /* # endif */
2126
2127 if (dabs (yr_int) > 0.0)
2128 {
2129 amortyr->year = yr++;
2130 amortyr->interest_pd = yr_int;
2131 amortyr->principal_pd = pv - hpv;
2132 amortyr->total_interest_pd = sum_int;
2133 amortyr->num_periods = pmt_cnt;
2134 } /* endif */
2135
2136 amortsched->total_periods = per_cnt;
2137 break;
2138 case 'o':
2139 /* Constant payment to principal use constant payment equal to
2140 * original pv divided by number of periods. constant payment to
2141 * principal could be amount specified by user. */
2142 amortsched->schedule.first_yr =
2143 amortyr = (amort_sched_yr_ptr) calloc (1, sizeof (amort_sched_yr));
2144 amortsched->total_periods = n;
2145
2146 d = yr_pmt;
2147 for (s = 1, j = n - 1; j; j--, k++)
2148 {
2149 pmt_int = -rnd (pv * eint, prec);
2150
2151 /* sum yearly interest paid */
2152 yr_int += pmt_int;
2153
2154 /* sum total interest paid */
2155 sum_int += pmt_int;
2156
2157 pv = rnd (pv + cpmt, prec);
2158
2159 if (sum_prt)
2160 {
2161 jj = (j < yr_pmt) ? j + 1 : yr_pmt;
2162 amortyr->payments =
2163 pmtsched = (sched_pmt_ptr) calloc (jj, sizeof (sched_pmt));
2164 amortyr->num_periods = jj;
2165 k = 0;
2166
2167 sum_prt = FALSE;
2168 } /* endif */
2169
2170 pmtsched->period_num = s++;
2171 pmtsched->interest = pmt_int;
2172 pmtsched->total_pmt = cpmt + pmt_int;
2173 pmtsched->balance = pv;
2174 pmtsched++;
2175
2176 if (!--yr_pmt)
2177 {
2178 yr_pmt = PF;
2179
2180 amortyr->year = yr++;
2181 amortyr->interest_pd = yr_int;
2182 amortyr->principal_pd = d * cpmt;
2183 amortyr->yr_end_balance = pv;
2184 amortyr->total_interest_pd = sum_int;
2185 amortyr->next_yr =
2186 (amort_sched_yr_ptr) calloc (1, sizeof (amort_sched_yr));
2187 amortyr = amortyr->next_yr;
2188
2189 d = PF;
2190 yr_int = 0.0;
2191 sum_prt = TRUE;
2192 } /* endif */
2193 } /* endfor */
2194
2195 if (pv)
2196 {
2197 pmt_int = -rnd (pv * eint, prec);
2198
2199 /* sum yearly interest paid */
2200 yr_int += pmt_int;
2201
2202 /* sum total interest paid */
2203 sum_int += pmt_int;
2204 if (pmtsched)
2205 {
2206 pmtsched->period_num = s++;
2207 pmtsched->interest = -pmt_int;
2208 pmtsched->total_pmt = -pv + pmt_int;
2209 pmtsched->balance = 0.0;
2210 }
2211
2212 amortyr->final_pmt = -pv - pmt_int;
2213 } /* endif */
2214
2215 if (dabs (yr_int) > 0.0)
2216 {
2217 amortyr->year = yr++;
2218 amortyr->interest_pd = yr_int;
2219 amortyr->principal_pd = -pv + k * cpmt;
2220 amortyr->total_interest_pd = sum_int;
2221 } /* endif */
2222 break;
2223 case 'p':
2224 /* normal amortization schedule interest, principal and balance
2225 * per payment period */
2226 amortsched->schedule.first_yr =
2227 amortyr = (amort_sched_yr_ptr) calloc (1, sizeof (amort_sched_yr));
2228 amortsched->total_periods = n;
2229
2230 hpv = pv;
2231 for (s = 1, j = n - 1; j; j--)
2232 {
2233 /* basic equation for computing interest paid in payment period */
2234 pmt_int = -rnd ((pv + (amortsched->bp * pmt)) * eint, prec);
2235
2236 /* sum yearly interest paid */
2237 yr_int += pmt_int;
2238
2239 /* sum total interest paid */
2240 sum_int += pmt_int;
2241
2242 /* compute principal paid this payment period */
2243 prin = rnd (pmt - pmt_int, prec);
2244
2245 /* compute remaining pv and round to nearest cent */
2246 pv = rnd (pv + prin, prec);
2247
2248 if (sum_prt)
2249 {
2250 jj = (j < yr_pmt) ? j + 1 : yr_pmt;
2251 amortyr->payments =
2252 pmtsched = (sched_pmt_ptr) calloc (jj, sizeof (sched_pmt));
2253 amortyr->num_periods = jj;
2254
2255 sum_prt = FALSE;
2256 } /* endif */
2257
2258 if (fv_case)
2259 {
2260 pmtsched->period_num = s++;
2261 pmtsched->interest = pmt_int;
2262 pmtsched->balance = pv;
2263 pmtsched++;
2264 }
2265 else
2266 {
2267 pmtsched->period_num = s++;
2268 pmtsched->interest = pmt_int;
2269 pmtsched->principal = prin;
2270 pmtsched->balance = pv;
2271 pmtsched++;
2272 } /* endif */
2273
2274 if (!--yr_pmt)
2275 {
2276 yr_pmt = PF;
2277
2278 amortyr->year = yr++;
2279 amortyr->interest_pd = yr_int;
2280 if (!fv_case)
2281 {
2282 amortyr->principal_pd = pv - hpv;
2283 } /* endif */
2284 amortyr->yr_end_balance = pv;
2285 amortyr->total_interest_pd = sum_int;
2286 amortyr->next_yr =
2287 (amort_sched_yr_ptr) calloc (1, sizeof (amort_sched_yr));
2288 amortyr = amortyr->next_yr;
2289
2290 hpv = pv;
2291 yr_int = 0.0;
2292 sum_prt = TRUE;
2293 } /* * endif */
2294 } /* * endfor */
2295
2296 /* determine if payment due at beginning or end of period in order
2297 * to correctly compute final payment, interest and principal */
2298 if (bep)
2299 {
2300 /* paying remainder at beginning of period compute final payment */
2301 final_pmt = -pv - fv / (1 + eint);
2302
2303 /* then compute interest paid with final final payment */
2304 pmt_int = -rnd ((pv + final_pmt) * eint, prec);
2305
2306 /* then compute the principal paid */
2307 prin = final_pmt + pmt_int;
2308 }
2309 else
2310 {
2311 /* basic equation for computing interest paid in payment period
2312 * for payment at end of period */
2313 pmt_int = -rnd (pv * eint, prec);
2314
2315 /* compute principal paid this payment period */
2316 prin = -pv;
2317
2318 /* compute the final payment note the final payment may be
2319 * computed either of two ways both are equivalent */
2320 final_pmt = prin + pmt_int;
2321 } /* * endif */
2322
2323 pv = -fv;
2324
2325 /* sum yearly interest paid */
2326 yr_int += pmt_int;
2327
2328 /* sum total interest paid */
2329 sum_int += pmt_int;
2330
2331 if (sum_prt)
2332 {
2333 amortyr->payments =
2334 pmtsched = (sched_pmt_ptr) calloc (1, sizeof (sched_pmt));
2335 amortyr->num_periods = 1;
2336 } /* endif */
2337
2338 amortyr->final_pmt = final_pmt;
2339
2340 if (fv_case)
2341 {
2342 pmtsched->period_num = s++;
2343 pmtsched->interest = pmt_int;
2344 pmtsched->balance = pv;
2345 }
2346 else
2347 {
2348 pmtsched->period_num = s++;
2349 pmtsched->interest = pmt_int;
2350 pmtsched->principal = prin;
2351 pmtsched->balance = pv;
2352 } /* endif */
2353
2354 if (dabs (yr_int) > 0.0)
2355 {
2356 amortyr->year = yr++;
2357 amortyr->interest_pd = yr_int;
2358 amortyr->total_interest_pd = sum_int;
2359 if (!bep)
2360 {
2361 amortyr->principal_pd = -hpv;
2362 } /* endif */
2363 } /* endif */
2364
2365 break;
2366 case 'x':
2367 /* constant payment to principal - annual summary */
2368 /* compute number of years to summarize */
2369 j = n / PF;
2370 if (yr_pmt < PF)
2371 j++;
2372 amortsched->total_periods = j;
2373 amortsched->schedule.summary =
2374 yrly_sum = (yearly_summary_ptr) calloc (j, sizeof (yearly_summary));
2375
2376 jj = 0;
2377 for (j = n, sum_prt = 0; j > 0; j -= yr_pmt, yr_pmt = PF, sum_prt++)
2378 {
2379 if (j <= PF)
2380 {
2381 s = jj + j;
2382 yr_pmt = j;
2383 yr_fv = rnd (pv + cpmt * (s - 1), prec) + final_pmt;
2384 }
2385 else
2386 {
2387 s = jj + yr_pmt;
2388 yr_fv = rnd (pv + cpmt * s, prec);
2389 } /* endif */
2390 prin = -eint * jj * (pv + (cpmt * (jj - 1) / 2.0));
2391 yr_int = -eint * s * (pv + (cpmt * (s - 1) / 2.0));
2392 yr_int = rnd (yr_int - prin, prec);
2393 jj += yr_pmt;
2394
2395 sum_int += yr_int;
2396
2397 yrly_sum[sum_prt].year = yr++;
2398 yrly_sum[sum_prt].interest = yr_int;
2399 yrly_sum[sum_prt].end_balance = yr_fv;
2400 } /* endfor */
2401
2402 break;
2403 case 'y':
2404 /* normal amortization - annual summary */
2405 /* compute number of years to summarize */
2406 j = n / PF;
2407 if (yr_pmt < PF)
2408 j++;
2409 if (n > (j * PF))
2410 j++;
2411 amortsched->total_periods = j;
2412 amortsched->schedule.summary =
2413 yrly_sum = (yearly_summary_ptr) calloc (j, sizeof (yearly_summary));
2414
2415 hpv = pv;
2416
2417 for (jj = n, j = 0; jj > 0; jj -= yr_pmt, yr_pmt = PF, j++)
2418 {
2419 if (jj <= (int)PF)
2420 {
2421 yr_fv = fv;
2422 yr_int = rnd (((jj - 1) * pmt) + hpv + final_pmt, prec);
2423 }
2424 else
2425 {
2426 yr_fv =
2427 -rnd (_fi_calc_future_value
2428 (yr_pmt, nint, hpv, pmt, CF, PF, disc, bep), prec);
2429 yr_int = rnd ((yr_pmt * pmt) + hpv - yr_fv, prec);
2430 } /* * endif */
2431
2432 sum_int += yr_int;
2433
2434 yrly_sum[j].year = yr++;
2435 yrly_sum[j].interest = yr_int;
2436 yrly_sum[j].end_balance = yr_fv;
2437 hpv = yr_fv;
2438 } /* * endfor */
2439
2440 break;
2441 } /* * endswitch */
2442
2443 amortsched->total_interest = sum_int;
2444
2445 return amortsched;
2446} /* Amortization_Schedule */
2447
2448/* function to free dynamically allocated memory used for amortization
2449 schedule */
2450void
2451Amortization_free (amort_sched_ptr amortsched)
2452{
2453 amort_sched_yr_ptr amortyr, prst_yr;
2454
2455 switch (amortsched->summary)
2456 {
2457 case 'a':
2458 case 'f':
2459 case 'o':
2460 case 'p':
2461 for (amortyr = amortsched->schedule.first_yr; amortyr; amortyr = prst_yr)
2462 {
2463 if (amortyr->payments)
2464 free (amortyr->payments);
2465 prst_yr = amortyr->next_yr;
2466 free (amortyr);
2467 } /* endfor */
2468 break;
2469 case 'y':
2470 free (amortsched->schedule.summary);
2471 break;
2472 } /* endswitch */
2473
2474 amortsched->schedule.first_yr = NULL;
2475} /* amort_free */
amort_sched_yr
Definition finvar.h:142
sched_pmt
Definition finvar.h:128
yearly_summary
Definition finvar.h:117
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