# How to Calculate a Loan Repayment Amount

Banks charge interest on loans.

When you take out a loan, you must usually repay it over a set period of time at a set interest rate. Using the amount borrowed, the interest rate and the term of the loan, lenders will calculate the monthly payment that you must make in order to pay off the loan in full. Each payment will go partially toward paying off interest and whatever remains will go towards paying down the balance of the loan. Once you know the monthly payments, you can calculate the total amount you will have to repay over the life of the loan. The most common formula uses a periodic interest rate, which is the interest rate on the loan per compounding period. Since most loans compound interest monthly, the example uses monthly interest compounding rather than annual interest compounding.

## Step 1

Add 1 to the periodic rate expressed as a decimal. For example, if your loan required monthly payments, the periodic rate would be found by dividing the annual rate by 12 so if the annual rate was 12 percent, you would divide 0.12 (12 percent expressed as a decimal) by 12 to get 0.01 and then add 1 to get 1.01.

## Step 2

Calculate the number of payments you will make to pay off the loan. For example, if you make monthly payments over seven years, you would multiply seven times 12 to find you would make 84 monthly payments.

## Step 3

Raise the result from step 1 to the power of the result from step 2. In this example, you would raise 1.01 to the 84th power to get 2.306722744.

## Step 4

Multiply the result from step 3 by the periodic rate. Continuing the example, you would multiply 2.306722744 by 0.01 to get 0.023067227.

## Step 5

Subtract 1 from the result from step 3. In this example, you would subtract 1 from 2.306722744 to get 1.306722744.

## Step 6

Divide the result from step 4 by the result from step 5. In this example, you would divide 0.023067227 by 1.306722744 to get 0.01765273.

## Step 7

Multiply the result from step 6 by the amount borrowed to calculate the monthly payment amount. In this example, if you borrowed \$22,000, you would multiply 0.01765273 by \$22,000 to find the monthly payment to be \$388.36.

## Step 8

Multiply the monthly payment by the number of monthly payments made over the life of the loan to calculate the total repayment amount of the loan. Finishing this example, you would multiply \$388.36 by 84 to find that over the life of the loan you would pay \$32,622.25.

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