How to Determine a Monthly Mortgage Payment

When you are trying to wade through the complexities of buying a home, you need to know how much house you can afford. That's determined partly by the price of the home, partly by the term of the loan and partly by the interest rate. The three together will determine the monthly payment. The basic equation used to compute the monthly payment is M = P[ i(1 + i)^n ] / [ (1 + i)^n - 1]. "M" is the monthly payment, "P" is the principal (the amount you are borrowing), "i" is a monthly interest rate you compute from your annual percentage rate (APR), and "n" is the number of months in the term of the loan.

Step 1

Determine an estimated loan amount and expected interest rate, or APR. The loan amount might be the price of the home, minus your down payment, and the interest rate could be based on general market rates or a rate for which you already know you can qualify. Let's base our example on a 30-year loan for $300,000 at 4.5 percent APR.

Step 2

Convert your APR to decimal form and divide by 12. For example, .045 divided by 12 is 0.00375, so our equation now reads M = $300,000[0.00375(1 + 0.00375)^n ] / [ (1 + 0.00375)^n - 1].

Step 3

Multiply the term of the loan in years by 12 to get "n." In our example: 30 years times 12 is 360. Our equation now reads M = $300,000[0.00375(1.00375)^360 ] / [ (1.00375)^360 - 1].

Step 4

Compute the "top" of the equation. In our example, we raise 1.00375 to the power of 360 and multiply the result by 0.00375. Our equation now reads M = $300,000[0.01429] / [ (1.00375)^360 - 1].

Step 5

Compute the "bottom" of the equation by raising 1.00375 to the power of 360 and then subtracting 1. Our equation now reads M = $300,000[0.01429] / [2.8477].

Step 6

Finish the arithmetic to get the monthly payment: $300,000 times 0.01429 is $4,287 and $4,287 divided by 2.8477 equals a monthly payment of $1,505.43.

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