You can use an online loan payoff calculator to determine how long it will take to pay off a loan based on the size of the payments you make at various times, or you can use a loan payoff formula to do the math yourself. Understand the terms of the loan, and whether there's any prepayment penalties or other factors beyond the principal and interest rate that affect these calculations.
Using a Loan Payoff Formula
If you've taken out a loan at a steady interest rate, it's usually pretty simple to figure out how many months or years it will take to pay off the loan. You can apply a standard loan payoff equation yourself using a calculator or a spreadsheet program, or you can use online loan calculators or standardized formulas in spreadsheet tools.
It can be helpful to use a loan payoff formula or calculator to figure out how much money you'll save and how quickly you'll pay off a loan if you pay more than the required minimum monthly payment. Often, it's worth paying off loans at high interest rates quickly to save money, but you may prefer to keep money in a savings account or other investments instead so you'll have it in case of an emergency.
In some cases, as with many credit card accounts, lenders may also include a report on your statement or on their online banking portals and apps telling you how long it will take to pay back a loan depending on the size of the payment you make each month.
If you have a variable line of credit or credit card account, where you can borrow additional money through your account if you wish, keep in mind that the loan payback formulas assume that you won't borrow any additional money on your account. If you do so, you'll have to pay more in interest and principal and it may take longer to pay back your loan.
The Loan Payoff Formula
If you want to calculate the number of payments you'll need to make on a loan, you'll need to know the amount currently owed on the loan, the size of the payments you're going to make on the loan and the interest rate on the loan. You can usually find the interest rate and the amount you owe in your loan documentation, on your latest statement or through the lender's online payment portal.
The standard loan payoff formulas use the natural logarithm function, a mathematical function that's useful for handling compound interest. You don't have to know the details of how logarithms work, but you will need a calculator or a computer program that can handle logarithms. Many scientific calculators and calculator apps can work with logarithms, as can most spreadsheet programs including Google Sheets and Microsoft Excel.
The loan payoff equation is N = (-log(1- i * A / P)) / log (1 + i). N represents the number of payments you must make, and i is the interest rate. A is the amount owed and P is the size of each payment. Since most loans require you to make payments every month, you will often want to use the monthly interest rate to calculate the number of monthly payments. If you only have an annual interest rate, divide it by 12 to get the monthly rate, since there are 12 months in a year.
Then, N will be the number of months you will take to pay off the loan. Divide N by 12 to get the number of years needed to make payments before the loan is paid off.
Spreadsheet Formulas and Online Calculators
Another option is to use an online calculator to determine your loan payback schedule based on the size of your payments. Your lender's site might provide one, or you can access them from financial information sites like Money Under 30 or Bankrate. Input the details of your loan and expected payment to determine how long you will take to pay off the loan. Don't give personal financial information to sites you don't trust.
You can also use the spreadsheet formula function NPER to determine the number of payment periods left on a loan. It's included in popular spreadsheet tools like Google Sheets and Microsoft Excel. Check the documentation for your preferred spreadsheet program to see if it's included and how to use it.
When to Pay Loans Early
You can often use a formula to calculate the time to pay off a loan, but you should make sure you understand the terms of the loan before simply plugging numbers into a loan payoff formula or online loan payoff calculator.
For some loans, such as loans on a credit card, it's generally the case that the more you pay upfront, the less interest you'll have to pay and the faster the loan will be paid off. In those cases, you can save money by paying the loan back early if you're able to do so. But some loans include what are called prepayment penalties, meaning that even if you pay off the loan by making more than your required minimum monthly payments, you will still owe a minimum amount in total interest before the loan is paid off.
While it may still be useful to you to have the loan paid off and not have to worry about it, you should make sure you understand the prepayment penalties and whether it makes sense to use the money to pay the loan off early rather than keeping it available for other purposes and to earn interest. Study the terms of your loan carefully to understand whether there's an advantage to paying early and what that advantage might be. If you're taking out a new loan, make sure you understand the ins and outs of the terms and conditions, including how the interest rates are determined and what any prepayment penalties might be.
Additionally, some loans have variable interest rates, including adjustable-rate mortgages and many credit cards. This can add some uncertainty to how much you will pay in total and potentially when you will have paid off all the interest and principal on a loan. Additionally, if a loan begins with a period in which you are not charged interest, as with some zero-percent financing deals and credit card deals, it may not make sense to pay a loan back early.
Understanding Required Minimum Payments
Keep in mind that most loans have a minimum monthly payment you must make, and if you fail to meet that requirement, you may face penalties and additional consequences, such as a hit to your credit rating. If the loan is backed by property, as with a car loan or a home mortgage, your lender might try to seize that property if you don't keep up with the loan. The lender may also sue you if you don't keep up with the terms of the loan.
If, for some reason, you can't make the required minimum payments on a loan, you may be able to work with the lender to establish a more lenient payment schedule. If you have more debt in general than you can pay off, you may want to consult with a lawyer to consider bankruptcy and other options.
- Fundera: Prepayment Penalty: What Happens If You Pay Off Your Loan Early?
- Money Under 30: Loan Payoff Calculator
- Bankrate: Auto Loan Early Payoff Calculator
- Google Support: NPER
- BrownMath: Loan or Investment Formulas
- ExcelJet: Calculate Payment Periods for Loan
- Microsoft: NPER Function
- Debt.org. "What Is a Loan Agreement?" Accessed Oct. 23, 2020.
- U.S. Department of Education Federal Student Aid. "The Standard Repayment Plan is the basic repayment plan for loans from the William D. Ford Federal Direct Loan (Direct Loan) Program and Federal Family Education Loan (FFEL) Program." Accessed Oct. 23, 2020.
- Corporate Finance Institute (CFI). "Amortization Schedule." Accessed Oct. 23, 2020.
- Consumer Financial Protection Bureau. "What is a prepayment penalty?" Accessed Oct. 23, 2020.
- Consumer Financial Protection Bureau. "Loan Estimate and Closing Disclosure: Your guides in choosing the right home loan." Accessed Oct. 23, 2020.
- Consumer Financial Protection Bureau. "What is a balloon payment? When is one allowed?" Accessed Oct. 23, 2020.
- Accion.org. "2 Different Types of Personal Guarantees Your Business Needs to Understand." Accessed Oct. 23, 2020.
- Consumer Financial Protection Bureau. "Know what is negotiable." Accessed Oct. 23, 2020.
- This information applies to standard loans only. Loans with adjustable interest rates or a balloon payment at the end would not use this formula.
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.