(11C) Loan Repayments

[Gamo]

Program to calculate for "Loan Repayments"

n = number of payments
i = Interest Rate in Percent
PMT = Payment
PV = Principal

Formula Used:

   

Procedure:

Interest Rate [A] Principal [R/S] Payment [R/S] --> Answer

Example:

This Example is from HP-38C Owner's Handbook.

Bill Buckskin wished to invest in a $22,000 log carbin to keep the rain off.
A local merchant has offered to loan Bill the $22,000 at 10.5% interest.
Making $200 monthly payments, how long will it take Bill to repay his mortgage?

10.5 [A] 22000 [R/S] 200 [R/S] --> 376.89

Answer:
376.89 // Months
12 ÷ Answer 31.41 // Years

Program:

Code:


LBL A
EEX 2
÷
12
÷
STO 0
R/S
x
R/S
÷
1
X<>Y
-
1/x
LN
RCL 0
1
+
LN
÷
RTN

Gamo

[Albert Chan]

(11-13-2018 01:37 PM)Gamo Wrote:  This Example is from HP-38C Owner's Handbook.

Bill Buckskin wished to invest in a $22,000 log carbin to keep the rain off.
A local merchant has offered to loan Bill the $22,000 at 10.5% interest.
Making $200 monthly payments, how long will it take Bill to repay his mortgage?

10.5 [A] 22000 [R/S] 200 [R/S] --> 376.89

You might want to rearrange the order, to get more information from same calculation.

22000 [Enter] 200 / --> 110.00, number of payments if no interest
10.5 [R/S]               --> 376.89, effect of 10.5% interest. 277 payments (23 years) just for interest !

[Gamo]

Thanks Albert Chan
Very good touch up.

Gamo

[Dieter]

(11-13-2018 01:37 PM)Gamo Wrote:  Formula Used:

image: "n = log 1 + i · [1 / (1 – PV · i / PMT)]"

No, that's not the formula. The "1+i" part must be a subscript after the log, indicating that the base 1+i logarithm of the bracketed term is calculated.

But the program uses a correct formula. I'd write it this way:
\[\begin{align}
n~&=~-log_{~1+i}~(1-\frac{i \cdot PV}{PMT}) \\
\\
&=~ -\frac{ln(1-\frac{i \cdot PV}{PMT})}{ln(1+~i)}
\end{align}\]

This is what the program correctly implements. Assuming that the user enters the monthly payment and the annual interest rate.

Dieter