# How Long Will It Take to Pay Off a Loan?

## Calculating the Loan Period Length from the Principal, Interest, and Monthly Payments

 Annual Interest Rate % Monthy Payment \$ Principal \$ months

If you know the principal of a loan (amount of money borrowed), the interest rate, and the size of the monthly payments, some natural questions to ask are "How long will it take me to pay down my auto loan?" or "How long will I be paying off my mortgage?" To answer these questions, you need to use a mathematical formula to calculate the loan period length. This article will show you how to compute the length of a loan term by hand, or you can use the calculator on the left.

First, estimate what you can afford to pay each month for your home loan or car loan, and call this number M. Estimate of the annual interest rate you are likely to qualify for, and call this number R. For the calculator, enter R as a percent. For the equation below, you must enter R as a decimal. For example, 7% = 0.07. Lastly, call the amount of money you intend to borrow P.

Now, use this formula to calculate N, the number of months in the loan period:

Log(M) - Log(M - PR/12)
N = ---------------------------------
Log(1 + R/12)

You can use either the "Log" or "Ln" button on your calculator, just make sure to use the same button for each of the three terms. (Log is logarithm in base 10; Ln is logarithm in base e = 2.71828.)

## Examples of Loan Period Computations

Suppose you want to borrow \$100,000 for a home mortgage, you can afford to pay \$800 a month, and with your credit score you can secure an interest rate of 7% annually. To figure out how long it will take to pay down this home loan, we set P = 100000, M = 800, and R = 0.07.

Log(800) - Log(800 - 7000/12)
N = -----------------------------------------
Log(1 + 0.07/12)

= 0.5673/0.002526
= 224.6

Since 224 months is about 19 years, a loan with these terms can be paid off in less than 20 years.

Suppose you want to borrow \$20,000 for a car loan, you can afford \$450 car payments every month, and the best interest rate you can obtain is 6% annually. We have P = 20000, M = 450, and R = 0.06.

Log(450) - Log(450 - 1200/12)
N = -----------------------------------------
Log(1 + 0.06/12)

= 0.1091/0.002166
= 50.4

Fifty months is about 4 years to pay off an auto loan.