Though you might not want to, many people have to take out a car loan to finance their purchase. Car loans generally range from three to five years, but that doesn't mean you're stuck with the loan for the entire term. Paying off the loan early can save you on interest, because you owe the money for a shorter period of time. To figure how long it will take before you pay off the loan, you need to know your interest rate, how much you owe and how much you'll pay per month.
Divide the annual interest rate, expressed as a decimal, by the number of payments you make per year. For example, say your annual rate is 6.6 percent and you pay monthly. Divide 0.066 by 12 to get a periodic interest rate of 0.0055.
Multiply the result by the amount remaining on your car loan. For example, say you still owe $12,000. In this example, multiply 0.0055 by $12,000 to get $66.
Divide the result by the monthly payment you plan to make to pay off your car loan. For this example, say you plan to pay $350 a month. Divide $66 by $350 to get 0.188571429.
Subtract the result from 1. In this example, subtract 0.188571429 from 1 to get 0.811428571.
Calculate the negative log of the result with a calculator. This is the numerator in the final fraction. In this example, the log of 0.811428571 is negative 0.090749704, so you get 0.090749704.
Add 1 to the periodic interest rate. In this example, add 1 to 0.0055 to get 1.0055.
Calculate the log of the result with a calculator. This is the denominator in the final fraction. In this example, the log of 1.0055 is 0.002382075.
Divide the numerator by the denominator to find the number of months it will take you to pay off your car. In this example, divide 0.090749704 by 0.002382075 to get 38.09691419, meaning that it will take just over 38 months to pay off your loan if you make $350 monthly payments.
