## Sunday, December 18, 2022

### HP Prime: Constant Payment Applied to Principal

HP Prime:  Constant Payment Applied to Principal

Constant Amount Applied to Principal

In most loans and mortgages,  the amount of payment applying to interest and principal depends on the running balance.

This program assumes the customer wants an equal portion to apply to principal each payment.   As a result, the payment itself, principal and interest, will vary.  The simple algorithm to amortize this loan is this:

For K=1 to N:

Int =  Bal * I%÷100

Tpmt = Int + CPMT

Bal_k = Bal_(k-1) - CMPT

where:

Bal = balance of a loan

PV = loan amount

CPMT = amount to be applied to principal each payment

I% = interest rate

Int = interest calculated for payment K

Tpmt = total payment for payment K

HP Prime Program CPYMT

The result of CPYMT is a four column matrix with rows:  k, interest in payment k, total payment k, resulting balance.  Keep in mind that program asks for periodic interest rate.

EXPORT CPYMT()

BEGIN

// 2022-10-24 EWS

// fix 2

HFormat:=1;

HDigits:=2;

// local

LOCAL n,i,p,b,it,tp,k,x;

LOCAL ll,l0,l1,l2,l3,m;

// main

INPUT({n,i,p,b},"Constant Principal",

{"N = ","I%=","PMT=","LOAN="},

{"# of payments",

"periodic interest rate",

"constant payment",

"loan amount"});

l0:={0};

l1:={0};

l2:={b};

FOR k FROM 1 TO n DO

it:=b*i/100;

tp:=p+it;

b:=b-p;

ll:=MAKELIST(x,x,1,n+1,1);

l0:=CONCAT(l0,{it});

l1:=CONCAT(l1,{tp});

l2:=CONCAT(l2,{b});

END;

l3:=CONCAT(ll,l0);

l3:=CONCAT(l3,l1);

l3:=CONCAT(l3,l2);

m:=list2mat(l3,SIZE(l0));

m:=TRN(m);

RETURN m;

END;

Example

Five year loan of \$10,000 where the customer requests an equal amount of principal to be applied each annual payment (\$2,000 a year).  The loan rate is 6.99%.

Inputs:

N = 5

I% = 6.99

PMT = 2,000.00

LOAN = 10,000.00

Result:

Year 1:  Interest:  \$699.00;  Total Payment:  \$2,699.00;  Balance:  \$8,000.00

Year 2:  Interest:  \$599.20;  Total Payment:  \$2,559.20;  Balance:  \$6,000.00

Year 3:  Interest:  \$419.40;  Total Payment:  \$2,419.40;  Balance:  \$4,000.00

Year 4:  Interest:  \$279.60;  Total Payment:  \$2,279.60;  Balance:  \$2,000.00

Year 5:  Interest:  \$139.80;  Total Payment:  \$2,139.80;  Balance:  \$0.00

Source

"Constant Payment to Principal Loan"  HP-41 User's Library Solutions: Lend/Lease/Savings  Hewlett Packard.  November 1980

Next week I am going to cover the legendary HP 75C.

All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

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