# Installment Loan Formula

by Kimberly Goodwin ; Updated July 27, 2017Installment loans have a fixed monthly payment amount through the the entire term of the loan and are the most common types of loans consumers encounter. Common types of installment loans include car loans, mortgages, student loans and personal consumer loans. In order to calculate the payment on an installment loan you simply need to know the amount borrowed, the interest rate and the number of payments you will make on the loan.

The formula for calculating the payment on an installment loan looks like this:

Payment = [ r x PV ] / [ 1 - ( 1 + r )^{-n} ]

In this formula r is the annual interest rate divided by 12, PV is the loan amount, and n is the total number of payments on the loan. Although the formula looks complicated, a very simple example illustrates its use.

## Example

You borrow $5,000 at an interest rate of 5 percent. Interest compounds monthly, and you make monthly payments on this loan. For simplicity of the calculation, assume you will only make three monthly payments on the loan.

Multiply the monthly interest rate times the loan amount.

(.05 / 12 ) x 5000 = 20.83333

Add one plus the monthly interest rate. Then raise this answer to the power of -3.

[ 1 + ( .05 / 12 )]^{-3} = 0.98760

Subtract your answer in step 2 from 1.

1 - 0.98760 = 0.0124

Divide your result in step 1 by your result in step 3 to find your loan payment.

Payment = 20.83333 / 0.0124

Payment = 1680.11

Note: Installment loans generally have a minimum of 12 payments and in many cases the number of payments is something higher like 60, 120, or 360. Calculating this formula by hand would be quite cumbersome, but utilities such as spreadsheets and financial calculators make it easy to quickly complete the calculation.