Most loans are made for a specified period of time, such as a 30-year mortgage or a five-year car loan. However, you may determine you can afford to make higher payments to pay off the loan sooner and save money on interest. If you know the principal amount of the loan or credit card, interest rate and your intended monthly payment, you can calculate the time required to pay off the loan.
Determine the current principal balance of the loan. For an existing loan, you can find this amount on a recent statement or an online banking account, if you have one set up. You can also contact the financial institution directly to get your principal balance. For a new loan, the borrowed amount is your principal balance.
Find the interest rate of the loan. This will likely be referred to as the annual percentage rate. For an existing loan, the APR will be shown on the monthly statements. For a new loan, you can contact your financial institution or your loan documents for the percentage rate. If you're researching loans and don't have a loan yet, you can look online for current interest rate estimators.
Convert the provided APR to a monthly percentage rate. Start by dividing the interest rate by 100 to convert to a decimal value. An interest rate of 7.5 percent divided by 100 would give it a decimal value of 0.075. Convert this into a monthly percentage by dividing the decimal value by 12, representing the number of months in a year. In this case 0.075 / 12 = 0.00625.
Determine how much you plan -- and can afford -- to pay each month. For this calculation you need to pay the same amount each month. Paying more or less in a month will change the length of time required to pay off the loan.
Calculate the amount of time required to pay off the loan using the following formula: N = -log(1 - iA / P) / log(1 + i). N is the number of monthly payments required to pay off the loan. This is the number you are trying to calculate. i is the monthly interest rate. A is the amount of the loan principal balance. P is the monthly payment amount. Log is the mathematical logarithm that requires a scientific calculator or Excel spreadsheet to calculate.
Example: You have a $80,000 mortgage balance remaining with a 6 percent APR and plan to pay $1,600 per month until it is paid off. The monthly interest is 6 / 100 / 12 = 0.005. N = -log(1 - 0.005 * $80,000 / $1,600) / log(1 + 0.005) N = -log(1 - 0.25) / log(1.005) N = -log(0.75) / log(1.005) Any log base will give the same answer. This calculation uses base 10. N = 0.12494 / 0.00216 N = 57.84 This means it would take 57 months plus a smaller payment to pay off this mortgage. Divide by 12 to convert this to years. 57.84 / 12 = 4.82 years
- This information applies to standard loans only. Loans with adjustable interest rates or a balloon payment at the end would not use this formula.