How to Calculate: Mortgage Payment Formula

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You could easily figure out your monthly mortgage payment if lenders didn't charge interest on loans. That formula would simply involve dividing the mortgage balance by the number of monthly payments you need to pay off the debt. However, because lenders need to make money off of loans, you can expect to pay interest on a mortgage, which complicates the formula used to figure out monthly payments. To calculate mortgage payments and account for interest on a fixed-rate mortgage, you'll need to follow a few steps.

Set Up Your Formula

  • Let P represent the monthly principal and interest payment on the mortgage payment you want to calculate. You need to know the interest rate you are likely to get, or i, and represent i as a decimal. For example, a 5 percent interest rate is 0.05. You also need to know how many monthly payments you will need to make over the life of the loan, represented as n. For example, 180 payments on a 15-year mortgage or 360 payments on a 30-year term. Also, determine your loan amount, or L. For example, if you plan to buy a $300,000 home and you have 20 percent as a down payment, your loan amount is $240,000, or $300,000 less $60,000.

Find Monthly Interest

  • Your mortgage-payment calculation requires a critical step that converts your annual interest rate to a monthly interest rate. Divide the 5 percent annual rate by 12 months and you get 0.416 percent: 5 / 12 = 0.416 percent per month. You then must convert this monthly percentage rate to a decimal, or 0.00416. Use 0.00416 in the mortgage-payment formula for the value of i. Do not use 5 percent, or 0.05.

Plug Numerical Values Into Formula

  • The formula used to calculate monthly principal and interest payments on a fixed-rate loan in which the rate and, therefore, payment never changes, looks like this: P = [i L (1 + i)^n] / [(1 + i)^n - 1]. Plug in numerical values for a $240,000 loan at 5 percent paid over 360 months and the equation is: P = [0.00416 $240,000 (1 + 0.00416)^360] / [(1 + 0.00416)^360 - 1]. For the values you must divide, the equation looks like this: $4449.94760844 / 3.45707893473. The monthly payment rounded to the nearest dollar is $1,287.

Other Calculations to Consider

  • In addition to paying principal and interest on your mortgage, the lender may also require you to pay into an escrow impound account each month. An escrow account allows you to make your property tax and homeowners insurance payments along with your mortgage payment each month. Basically, your lender divides the total of your annual property taxes and insurance premium by 12 months and adds the amount to your mortgage payment. The lender then uses the installments accrued in your escrow account to pay the taxes and insurance on your behalf.

References

  • Photo Credit h-komm/iStock/Getty Images
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