Calculating Amortization of a Loan

Posted by Brendan Flaherty

May 31, 2016 3:30:29 PM

Assume you purchase a car for $20,000 at an 8% interest rate over a five-year period. What is the monthly payment?

I use the following grid to visualize the keystrokes on the HP-12C. As you see, the items are the same from left to right on your calculator. Enter the following to get a monthly payment of $405.52.

n i PV PMT FV
5 8% $25,000 ? $0
g – n g – i   g End  
= 60.0000 1= .6667   PMT Button  

Note: To get 4 decimal points on your HP-12C calculator, enter “f,” then “4.” Also, the “g – n” means 5 years times 12 or 5*12 for 60 months, whereas 8 “g – i” means 8% divided by 12 or a .6667 monthly interest rate. Lastly, it is redundant to enter $0 for future value, and “g End” means that “Begin” is not displayed on your HP-12C. I use this format for all TVM questions.

What is the remaining principal amount after 7 payments? (There are 2 methods to calculate)

Method 1 - Adjust your “n”

Take the original “n” of 60 compounding periods and subtract the 7 payments paid to date to arrive at a remaining “n” of 53. Enter 53 for “n” and enter “PV”. Your HP 12C will display a value of $18,056.1047.

Next, how much interest was paid?

Payment amount $405.52
Number of payments x 7 payments
Total payments made $2,838.64
Less: Principal paid ($20,000 – 18,056.10) (1,943.90)
Interest paid on the 7 payments $894.74

Method 2

Enter the original information given to get a monthly payment of $405.5279. Take the number of payments you want to amortize (7 in this example) and enter “7”, “f”, and “AMORT”, which is the “n” key. The number received is 894.7999, which rounds to $894.80 of interest.

To receive the amount of principal hit “X><y”><Y” again, you toggle back to the interest amount of $894.7999.

Note: The two different methods will create insignificant rounding differences.

Topics: Time Value of Money, Course 1: Intro to FP