# How to Calculate Mortgage Interest

The total interest on a mortgage is often greater than the amount borrowed.
Image Credit: AlexRaths/iStock/Getty Images

If you borrow \$200,000 at an interest rate of 6 percent per year, that's \$12,000 a year in interest. If the loan lasts 30 years, that's \$360,000 in interest. However, there is a more complex but favorable way to calculate the amount of interest you pay on a mortgage. It considers the fact that each time you make a payment, your loan amount decreases, and it charges you interest only on the money that you still have left to pay back.

## Number of Payments and Interest Rate

When you're calculating mortgage interest, the first input into the calculation is the length of your mortgage, or the number of payments you'll make on the loan. For example, a 30-year mortgage usually requires one payment a month for 30 years, or 360 payments. The next input into the calculation is the interest rate. Most lenders quote loan interest as an annual percentage. When you're making monthly payments, you need to convert the annual interest rate to a monthly interest rate by dividing it by 12. For example, if the annual interest rate is 6 percent, the monthly rate is half of 1 percent, or 0.005.

## Monthly Payment Amount

While your monthly mortgage payment usually remains the same, the amount of interest you pay each month is different. This makes the calculation of your monthly payment amount somewhat complex. To calculate the monthly payment including interest, use the formula A = P{r(1 + r)^n / [(1 + r)^n - 1]}, where A is the monthly payment, P is the amount of the loan, r is the monthly interest rate and n is the number of payments. For a \$200,000 loan at 6 percent interest over 30 years, P is 200,000, r is 0.005, and n is 360:

A = 200,000{0.005(1 + 0.005)^360 / [(1 + 0.005)^360 - 1]} = \$1,199.10

## Monthly Principal and Interest

With a typical mortgage, the amount of interest you pay each month goes down with each payment, because the lender charges interest only on the outstanding principal of the loan. For example, your first loan payment includes interest on the full amount of the loan, or 0.005 times \$200,000, which is \$1,000. If your monthly payment is \$1,199.10, then \$1,000 goes toward interest and \$199.10 toward principal. This brings the loan balance to \$199,800.90, the amount you'll pay interest on in your next payment. The total interest over 30 years is \$231,676.38.

## Amortization Schedule and Total Interest

In addition to the interest on a loan, many lenders charge fees, which are usually called closing costs on a mortgage. However, fees and interest rates vary among lenders, and it can be complicated to compare offers with different interest rates and different closing costs. To simplify this process, many lenders add the closing costs to the amount of the loan and provide you with an annual percentage rate of your loan that you can use to help select the best loan offer. For example, BankRate.com estimates closing costs on the example loan to be \$4,800, resulting in an APR of 6.223 percent.