What is the formula to determine loan repayment? I’m curious what the formula is to determine at a particular interest rate how much per thousand dollars borrowed will be due each month? I see amortization tables, for example, all the time. But how does the dollar amount get arrived at?

The simple interest formula for calculating interest on a loan is the interest rate (expressed as a fraction) divided by 365 (number of days in a year) times the loan amount times the number of days of interest accrual since the funding of the loan (for the first payment) or since the date of the last payment (for payments subsequent to the first payment). Calculate the interest amount for the first payment then reduce the principal amount of the loan by an equal fraction equating to the term of the loan (so, by 1/12th for a twelve-month term) and repeat the simple interest calculation on the reduced amount. Do this for each monthly payment until you’ve derived the total amount of interest payable on the loan and divide that total by the number of months in the loan term. Add that figure to the monthly principal amount (original principal amount divided by the loan term) and you have the payment amount needed to fully amortize the loan.

For the sake of an easy example, let’s take a $1000 loan amount for a 10 month term at 6% interest:

The calculation for the first payment would be:

.06/365x1000x30 = $4.93; then reduce the principal by 1/10th and repeat the calculation:

.06/365x900x30 = $4.44; then reduce the principal by 1/10th (of original amount) and repeat:

.06/365x800x30 = $3.95; repeat this calculation for each month in the loan term and you’ll derive $27.71 as the total amount of interest payable on the loan over the 10 month term (remember that some of the months will have 31 days).

Divide the total interest payable by the number of months in the term and the total principal by the number of months in the term and add those two figures together for the fully amortized payment amount:

$27.71/10 = $2.77

$1000/10 = $100.00

$2.77 + $100.00 = $102.77 = amount of the monthly payment to fully amortize the loan.

This is the hard way to derive the monthly payment amount for a loan. The easy way is to use an Excel spreadsheet and enter the proper formulas in the proper cells to create a loan payment calculator using the =PMT formula.

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