# 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.

## Adjustable Interest Rates

If your loan has an adjustable interest rate, the actual time it takes you to pay off the loan will vary depending on how interest rates change in the future. Unless you have a crystal ball -- in which case you probably wouldn't need to borrow money anymore -- there's no way to predict with certainty how interest rates are going to change. So, if the rate on your loan changes, you're going to have to run the numbers all over again. If the rate goes up, it'll take longer, but if it falls, you'll be debt-free faster.

## Prepayment Penalties and Add-on Interest

Sometimes lenders tack on extra penalties if you pay the loan off ahead of schedule. While you might still save money on interest, even after accounting for the penalty, you need to consider these extra costs. Worse, some lenders use "add-on interest" to figure your loan payments, which means that the interest is figured at the start of the loan and added to the balance immediately, so prepaying the loan doesn't decrease the amount of interest you'll pay over the life of the loan.