# How to Calculate the Number of Months to Pay Off a Loan

When you make monthly payments on a loan, it helps to know how long you have left to pay it off so you can better budget your money. By using a formula and some basic information about your loan, you can calculate the number of months until you're free of the debt. This formula works for a typical mortgage, auto loan or personal loan that is fully amortizing, which means its payments include both principal and interest and its balance reduces to zero over a fixed term.

#### Things You'll Need

• Most recent loan statement

• Scientific calculator

## Step 1

Find your monthly principal and interest payment, outstanding balance and annual interest rate on your most recent loan statement. Exclude any property taxes, insurance or other charges from the payment.

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For example, assume you have a 30-year mortgage with a current balance of \$167,371.45, a monthly payment of \$1,199.10 and a 6 percent annual interest rate.

## Step 2

Divide your annual interest rate by 12 to calculate your monthly interest rate.

In the example, divide 0.06 by 12 to get a monthly interest rate of 0.005:

0.06 / 12 = 0.005

## Step 3

Substitute the loan balance, monthly payment, and monthly interest rate into the loan term formula:

N = –[ln(1 – [(PV * i) / PMT_] ) / ln(1 + _i)]

In the formula, "ln" stands for natural logarithm, a math function used to calculate exponents. The formula also contains four variables:

N = the number of months remaining

PV = present value, or outstanding loan balance

PMT = monthly payment

i = monthly interest rate

In the example, substitute \$167,371.45 for PV, \$1,199.10 for PMT and 0.005 for i:

N = –[ln(1 – [(\$167,371.45 * 0.005) / \$1,199.10] ) / ln(1 + 0.005)]

## Step 4

Multiply the balance by the monthly interest rate and divide the result by the monthly payment in the numerator.

In the example, multiply \$167,371.45 by 0.005 to get \$836.86. Divide \$836.86 by \$1,199.10 to get 0.6979.

N = –[ln(1 – 0.6979) / ln(1 + 0.005)]

## Step 5

Subtract the figures in parentheses in the numerator, and add the figures in the parentheses in the denominator.

In the example, subtract 0.6979 from 1 to get 0.3021 in the numerator. Add 1 and 0.005 to get 1.005 in the denominator:

N = –[ln(0.3021) / ln(1.005)]

## Step 6

Input the figure in parentheses in the numerator into the scientific calculator, and push the natural logarithm button, "ln," to calculate the natural logarithm in the numerator.

In the example, input "0.3021" in the calculator, and push "ln" to get –1.197:

N = –[–1.197 / ln(1.005)]

## Step 7

Input the figure in parentheses in the denominator into the calculator, and push the natural logarithm button to figure the natural logarithm in the denominator.

In the example, input "1.005" in the calculator, and push "ln" to get 0.00499:

N = –(–1.197 / 0.00499)

## Step 8

Divide the remaining figures in parentheses.

In the example, divide –1.197 by 0.00499 to get –239.9:

N = –(–239.9)

## Step 9

Apply the negative sign outside the parentheses to the number in parentheses to calculate the number of months remaining on your loan.

In the example, apply the negative sign to –239.9 to get positive 239.9, or approximately 240 months left on the loan:

N = 240

This means if you make all your payments on time, you will pay off the loan in 240 months, or 20 years, from the current month.