Installment Loan Formula

An installment loan is a loan that you pay off in a steady number of same-size payments over a fixed period of time. The size of each payment is determined so that the loan is paid off at the end of the loan period. Ordinarily, your lender will tell you the amount that you need to pay each month, but if you need to calculate this number yourself, you can do so using a relatively simple mathematical formula, an online calculator tool or a spreadsheet function.

What's an Installment Account?

An installment loan is one that you pay off over time, usually making the same payment each month for a fixed number of months. Many loans operate this way, including many mortgages that you use to buy houses and real estate and many auto loans that you use to buy vehicles. Some consumer loans also work this way, such as loans you take out to buy appliances or other household goods. Typically, you must make a payment on an installment loan each month, but they can have other periods as well where you must make payments.

An installment loan differs from a revolving credit account, such as a credit card or certain personal and business lines of credit that let you borrow money up to a credit limit and pay it off at a schedule of your choice. If you stop borrowing money on a revolving credit account and resolve to pay it off through fixed payments over a certain amount of time, it will effectively function like an installment loan.

Generally, a lender will tell you how much you owe each month, but if you want to verify this number or you have lent someone money and want to tell them how much to pay you each month, you can use a standard installment loan formula to determine the monthly payment for the installment loan.

Understanding the Installment Formula

Assuming you have an installment loan where you know the principal, or initial amount borrowed, and the interest rate and the number of months to pay off the loan, you can use the installment payment formula to figure out how much you must pay each month.

The formula looks like:

P = r (V) / (1 - (1 + r)-n)

where P is the monthly payment, V is the amount borrowed, r is the monthly interest rate and n is the number of months to pay off the loan. If you only have an annual interest rate, as is published for many loans, divide it by 12 to find the monthly interest rate, since there are 12 months in a year. You can compute the formula using a physical or online calculator or with a spreadsheet program.

Note that the formula doesn't work for interest-free loans since it will result in dividing by zero. For a no-interest loan, you can simply divide the principal amount by the total number of months to pay off the loan and pay that amount each month.

Installment Loan Payment Calculator Tools

If you don't want to plug numbers into the formula directly, you can find many online installment loan payment calculator tools that will do it for you. Simply enter the numbers for the interest rate, the number of payment periods and principal to compute the monthly payment.

If you use Microsoft Excel, the popular spreadsheet tool, you can also use the built-in formula function called PMT to compute the payment amount. This function is also included in other popular spreadsheet programs, including Google Sheets. Read your spreadsheet program's manual to see the details of how its version of PMT works.

References

About the Author

Steven Melendez is an independent journalist with a background in technology and business. He has written for a variety of business publications including Fast Company, the Wall Street Journal, Innovation Leader and Ad Age. He was awarded the Knight Foundation scholarship to Northwestern University's Medill School of Journalism.