# How to Calculate How Fast a Loan Will Pay Off

Typically, loans come with a preset term for you to pay off the balance, such as three to five years for a car loan or 15 to 30 years for a mortgage. However, if you're planning to make extra payments, you can pay off the loan even faster. How much faster depends on the interest rate, how much you owe and how often you make payments.

## Formula

To start, first figure the periodic interest rate on your loan by dividing the annual rate as a decimal by the number of payments you make per year. Second, multiply the periodic rate by the amount you owe. Third, divide the result by the amount you pay each month. Fourth, subtract the result from 1. Fifth, take the log of the result and then make the result positive -- hold on to that number, you'll need it in a few steps. Sixth, add 1 to the periodic rate as a decimal. Seventh, take the log of the result. Finally, divide the result from step 5 (you've been holding on to it, right?) by the result to find the number of payments you have to make until the loan is paid off.

## Example

Suppose you have a \$25,000 loan at 6.6 percent interest that you make \$600 monthly payments on. First, divide 0.066 by 12 to find the periodic interest rate equals 0.0055. Second, multiply 0.0055 by \$25,000 to get \$137.50. Third, divide the result by 0.0055 to get 0.229166667. Fourth, subtract 0.229166667 from 1 to get 0.770833333. Fifth, take the log of 0.770833333 to get -0.113039513 and make it positive to get 0.113039513. Sixth, add 1 to 0.0055 to get 1.0055. Seventh, take the log of 1.0055 to get 0.002382075. Finally, divide 0.113039513 by 0.002382075 to get 47.45, meaning it will take just over 47 months to pay off the loan.