How To Calculate Mortgage Payments

If you have ever bought a home, or thought of buying a home, you’ve probably wondered about how to calculate mortgage payments. These days mortgages come in all shapes and sizes, each with their own intricacies. Understanding these intricacies is necessary to properly calculate mortgage payments and to determine how much house is affordable.

1. Understand the components of a mortgage payment. All mortgage payments can be broken down into two components: interest and principal. In a traditional fixed rate mortgage, there is a set monthly payment for the life of the mortgage (typically fifteen or thirty years). Most of the monthly payment goes to pay principal in the early part of the mortgage; however, by the end of the mortgage, most of the monthly payment goes to pay off principal.
2. Calculate the monthly interest rate. The effective monthly interest rate is simply the interest rate on the mortgage divided by twelve. For example, if you had a 6.00% mortgage rate, the monthly interest rate would be 6.00% / 12 = 0.50%. In decimal form, take the monthly interest rate percentage and divide by 100. Continuing the example above, 0.50% / 100 = 0.0050.
3. Calculate the monthly payment. To calculate the mortgage payment, use the monthly interest rate as described above. That interest rate can be placed into the following equation to determine the monthly mortgage payment: Monthly Payment = P[i(1 + i)ⁿ] / [(1 + i)ⁿ-1]. In this equation, P is the total mortgage amount, i is the monthly interest rate (in decimal form), and n is the number of months of the mortgage.
4. Understand this example. For example, if you had a 30 year $200,000 mortgage with a 5.50% interest rate, the calculation of the mortgage payments would be as follows. First, calculate the monthly interest rate: 5.50% / 12 = 0.4583% = 0.004583. Next, calculate the number of months of the mortgage: 30 years * 12 = 360 months. Finally, calculate the mortgage payment: Payment = ($200,000) [0.004583(1+0.004583)³⁶⁰] / [(1+0.004583)³⁶⁰– 1] = $1135.58.
5. Realize that the principal and interest is only one portion of a complete monthly payment. What was calculated above is only the principal and interest component of a monthly mortgage payment. Most monthly payments include additional bills for property taxes, homeowner’s insurance, and private mortgage insurance. Property taxes vary greatly depending on where you live; consult with a real estate agent or the previous owner to get an estimate of the annual and monthly property tax bill. Consult with the insurance company of your choice to determine monthly homeowner’s insurance payments. Finally, discuss private mortgage insurance payments with your mortgage lender—typically, private mortgage insurance is only required if your down payment is less than twenty percent of the home’s value.
6. To summarize, total monthly mortgage payments consist of PITI. PITI stands for principal, interest, taxes and insurance. Add all of these sums together to get the total monthly cost of living in a home.

Owning a home is a dream for many. Properly understanding how to calculate mortgage payments will help you avoid purchasing more (or less) home than you can afford. Use the techniques above to calculate your monthly principal and interest, and consult with real estate agents, previous owners, your mortgage company and insurance company to get the monthly amounts for taxes and insurance.

Reference:

University of Georgia, Department of Mathematics