# How to Calculate Mortgage Interest

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.

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## 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:

## 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.

## Adjustable Rate Mortgages

With an adjustable-rate mortgage, your interest rate is subject to change every so often. To calculate mortgage interest, **consider each period of the loan with a constant interest rate as a separate loan**. then sum the interest payments for each period. For example, if the interest rate is 4 percent for five years and then goes up to 5 percent, calculate the interest at 4 percent based on a five-year loan, then calculate the interest at 5 percent on a 25-year loan for the outstanding principal balance at the end of the first five-year period.

Category: Credit

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