我的任务是创建一个可以生成摊销计划的程序。到目前为止，我只做了一点研究，但我需要计算付款、每次付款的利息和每次付款的本金。任何人都可以指出我正确的方向来解决这个问题吗？虽然我将在 RPG 中编写这个，但我相信其他人将来可以使用这个算法。
（更新）好的，那么我如何根据一年 365 天计算？
【问题讨论】：
标签： algorithm language-agnostic amortization
当我最近买第一套房子时，我写了一个 JavaScript 应用程序供我个人使用。
这是我的代码修改后的 sn-p 以确定每月付款：
var balance = 200000; // for example
var periods = 360; // 30 years
var monthlyRate = (0.065)/12; // 0.065= APR of 6.5% as decimal
var monthyPayment = (monthlyRate /(1-(Math.pow((1+monthlyRate),-(periods)))))*balance;
for (var i=0; i<360; i++) {
var interestForMonth = balance * monthlyRate;
var principalForMonth = monthlyPayment - interestForMonth;
balance -= monthlyPayment; // probably should be -= principalForMonth see comments below
// output as necessary.
}
之后很容易制作摊销表。 （正如其他人所提到的，请注意舍入错误，我在实现中没有充分处理这个问题。）
【讨论】：
有很多网站提供这些公式。一个如下： http://www.math4finance.com/financial-formulas.php
不需要花哨的算法，因为公式通常很简单。
【讨论】：
C# 中的摊销时间表公式
numerator = i * principle * (Math.Pow(1 + i, n));
denominator = (Math.Pow(1 + i, n) - 1);
/* Calculation of Amortization Payment Amount */
payment = numerator / denominator;
【讨论】：
布赖恩是对的。公式很简单。
如果您希望您的解决方案是一个好的解决方案，您需要注意舍入误差。如果您只是让舍入误差累积并传播，您可以在计划结束时减少几美分。通过仔细编程，您将最大限度地减少错误。
另外，如果您的计算机上有 MS Excel，您可以从 MS Office 在线下载摊销模板。
【讨论】：
这是我最终创建的。我已经发布了整个测试程序。它是用 RPG 编写的，但对于任何其他语言都应该很容易理解。
H ActGrp(*caller) BndDir('MODULES') DftActGrp(*no)
//*********************************************************************
// Program . . . . . AMORT
//*********************************************************************
// Printer/Display Files
FAMORTDF CF E WORKSTN sfile(SFL01:rrn01)
//*********************************************************************
// Named Constants
/copy modules/qcopysrc,statuscopy
// Named Indicators
D indicatorPtr S * Inz(%Addr(*IN))
D DS Based(IndicatorPtr)
/copy modules/qcopysrc,scrncopy
// Subfile Fields
D rrn01 S 4P 0 inz(0)
//*********************************************************************
// Misc Fields
D* Monthly Payment
D m S 12P 2
D* Principal
D p S 12P 2
D* Interest
D i S 5P 3
D* Length (in Years)
D l S 3P 0
D* Monthly Interest
D j S 10P10
D* # of Months
D n S 5P 0
D* Current Monthly Int.
D h S 12P 2
D* Current Principal
D c S 12P 2
D* New Balance
D q S 12P 2
//*********************************************************************
// External Program Procedures
// Internal Subprocedures
D Init PR
D Main PR
D SubfileFilled PR N
D ClearScreen PR
D IsValidData PR N
D LoanPayment PR 12P 2
D principal 12P 2
D interest 5P 3
D loanPeriod 3P 0
D paymentsYear 3P 0
// External Subprocedures
///copy modules/qsrvsrc,p.string
//*********************************************************************
// Entry Parms
D AMORT PR extpgm('AMORT')
D AMORT PI
//*********************************************************************
/free
Init();
Main();
*inlr = *on;
/end-free
P*--------------------------------------------------
P* Procedure name: Init
P* Purpose:
P* Returns:
P*--------------------------------------------------
P Init B
D Init PI
/free
pgm = 'AMORT';
sflDsp = *off;
return;
/end-free
P Init E
P*--------------------------------------------------
P* Procedure name: Main
P* Purpose:
P* Returns:
P*--------------------------------------------------
P Main B
D Main PI
/free
dow (not F3) and (not F12);
write OVR01;
exfmt CTL01;
ClearScreen();
if (IsValidData()) and (not F3) and (not F12);
// Fill the header information
dPayment = LoanPayment(dLoanAmt:dIntRate:dLoanPrd:dPayYear);
dNumPaymnt = dLoanPrd * dPayYear;
m = dPayment + dExtraPay;
p = dLoanAmt;
q = p;
// Fill the table
if (SubfileFilled());
sflDsp = *on;
endif;
endif;
enddo;
return;
/end-free
P Main E
P*--------------------------------------------------
P* Procedure name: SubfileFilled
P* Purpose: Fill the subfile
P* Returns:
P*--------------------------------------------------
P SubfileFilled B
D SubfileFilled PI N
D isFilled S N
D x S 4P 0
D intCume S 12P 2
D extraPayCume S 12P 2
D payDate S D
D payment S 12P 2
D extraPayment S 12P 2
/free
isFilled = *on;
sflClear = *on;
write CTL01;
sflClear = *off;
rrn01 = 0;
x = 0;
// Setup the work fields
payment = dPayment;
extraPayment = dExtraPay;
payDate = dStartDate;
// Create records until there is a zero balance
dow (q > 0);
x += 1;
eval(h) h = p * j; // Monthly Interest
// Adjust for final payment
if (p < m);
m = p + h;
payment = p;
extraPayment = h;
endif;
// Calulate Principal
c = m - h;
// Calulate the new balance
q = p - c;
// Accumulate the interest and extra payments
intCume += h;
extraPayCume += extraPayment;
// Determine the next pay date
select;
when dTerms = '1'; //Yearly
payDate += %years(1);
when dTerms = '2'; //Semi-Annual
payDate += %months(6);
when dTerms = '3'; //Quarterly
payDate += %months(3);
when dTerms = '4'; //Monthly
payDate += %months(1);
when dTerms = '5'; //Bi-Weekly
payDate += %days(14);
endsl;
// Fill the subfile
sPayNum = x;
sPayDate = payDate;
sBegBal = p;
sSchedPay = payment;
sExtraPay = extraPayment;
sTotPay = m;
sInterest = h;
sPrincipal = c;
sEndBal = q;
sCumeInt = intCume;
// Move the End balance to the beginning balance
p = q;
rrn01 += 1;
write SFL01;
enddo;
// Return the calculated information to the header
dActPaymnt = x;
dTotInt = intCume;
dTotEPay = extraPayCume;
if (rrn01 < 1);
isFilled = *off;
endif;
return isFilled;
/end-free
P SubfileFilled E
P*--------------------------------------------------
P* Procedure name: ClearScreen
P* Purpose:
P* Returns:
P*--------------------------------------------------
P ClearScreen B
D ClearScreen PI
/free
c = 0;
h = 0;
i = 0;
j = 0;
l = 0;
m = 0;
n = 0;
p = 0;
q = 0;
dPayment = 0;
dNumPaymnt = 0;
dActPaymnt = 0;
dTotEPay = 0;
dTotInt = 0;
return;
/end-free
P ClearScreen E
P*--------------------------------------------------
P* Procedure name: IsValidData
P* Purpose: Validate the data on the screen
P* Returns: True or False
P*--------------------------------------------------
P IsValidData B
D IsValidData PI N
D isValid S N
/free
if (dLoanAmt <> 0) and (dIntRate <> 0) and (dLoanPrd <> 0) and
(dPayYear <> 0) and (dStartDate <> %date('0001-01-01'));
isValid = *on;
else;
isValid = *off;
endif;
return isValid;
/end-free
P IsValidData E
P*--------------------------------------------------
P* Procedure name: LoanPayment
P* Purpose: Calculates the payment
P* Returns:
P*--------------------------------------------------
P LoanPayment B
D LoanPayment PI 12P 2
D principal 12P 2
D interest 5P 3
D loanPeriod 3P 0
D paymentsYear 3P 0
D retMonthlyPayment...
D S 12P 2
/free
eval(h) n = loanPeriod * paymentsYear;
eval(h) j = interest / (paymentsYear * 100);
eval(h) m = principal * (j / (1 - (1 + j) ** -n));
return m;
/end-free
P LoanPayment E
此代码已针对我们的贷款计算器进行了测试。如果 test vs. Excel，200,000 美元的贷款减少了大约 32 美分。我确信这对四舍五入问题有帮助。
【讨论】：
var annuity = P * (i + i / (Math.pow(1+i,n) -1));
//P: principal, I: periodic interest rate, N: number of periods
【讨论】：