# How to Calculate the Number of Payments Left on a Loan

Calculating remaining loan payments helps with budgeting.

Borrowing money has become more prevalent, especially with the rising costs of a college education. Most people can track their loan payments online and determine how much money they must pay back and how many times they need to make the payment. If this is unavailable, there is a mathematical formula to determine how many more payments a loan holder must make.

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## Step 1

Determine the amount of remaining principal, payments and the interest rate on the loan. For example, a former student has \$20,000 remaining in principal on a college loan with 6 percent interest, and each month he pays \$300 on the loan. Translate the interest rate to the interest rate per month by dividing 6 percent by 12, which equals 0.005.

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## Step 2

Divide the principal of the loan by the payment amount. In our example, \$20,000 divided by \$300 equals 66.6667. Then multiply that number by the interest rate per month. In our example, 66.6667 times 0.005 equals 0.3333.

## Step 3

Subtract from 1 the number calculated in Step 2. In the example, 1 minus 0.3333 equals 0.6667.

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## Step 4

Add 1 to the interest rate per month. In our example, 1 plus 0.005 equals 1.005.

## Step 5

Calculate the negative logarithm of the number calculated in Step 3. Use a calculator with a logarithm function (see Resources). Plug in 0.6667 and hit the "log" key. In our example, -log(0.6667) equals 0.176070.

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## Step 6

Calculate the log of the number calculated in Step 4. In our example, log(1.005) equals 0.002166.

## Step 7

Divided the number calculated in Step 5 by the number calculated in Step 6 to determine the number of remaining payments. In our example, 0.176070 divided by 0.002166 equals 81.29. So the former student will have 81 remaining payments of \$300 and one payment of \$87 (.29 times \$300), for a total of \$24,387 (principal plus interest).

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