# How to Calculate a Lump Payment Sum

Calculating loan payoff

When a person takes out a loan, he usually agrees to pay the money back by paying a fixed fee each month. The person who took the loan out usually has the option to pay the loan back in one lump payment. In order to do that, the person needs to calculate the balance remaining on the loan. For example, a person took out a \$50,000 loan, payable back in 48 monthly payments of \$1,174.25. The interest rate on the loan is 6 percent and he made 11 payments on the loan.

## Step 1

Divide the interest rate by 12, add one to the interest then raise the amount to the power of the number of payments made on the loan so far, this is the interest factor. In our example, the interest factor is 6 percent divided by 12, which equals 0.005. Add 1 to 0.005 for 1.005. Then take 1.005 raised to the power of 11, which equals an interest factor of 1.056396.

## Step 2

Multiply the interest factor by the total amount borrowed. In our example, 1.056396 times \$50,000 equals 52,819.79.

## Step 3

Divide the monthly payment by the interest rate per month. In our example, \$1174.25 divided by 0.005 equals \$234,850.

## Step 4

Subtract 1 from the interest factor. In our example, 1.056396 minus 1 equals 0.056396.

## Step 5

Multiply the number calculated in Step 3 by the number calculated in Step 4. In the example, \$234,850 times 0.05696 equals \$13,377.06.

## Step 6

Subtract the number calculated in Step 5 from the number calculated in Step 2. In the example, \$52,819.79 minus \$13,377.06 equals \$39,442.73 which the borrower needs to pay back in one lump sum.

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