How to Calculate a Fixed Rate Mortgage

Fixed-rate mortgages (FRM) make up approximately 75 percent of the home-financing market. As the names suggests, the interest rate for an FRM remains constant throughout the term of the loan. This does not necessarily mean that the payments are constant. "Interest only" FRM's, for example, have a fixed interest rate, but the payments change after the interest-only period expires. While the term of a fixed-rate mortgage typically varies from 10 to 40 years, 15- and 30-year loans are the most common.

Instructions

Payment Calculation

1. Collect the information you will need for the calculations--the amount of the loan; the term of the loan, which is usually in years; and the annual percentage rate (APR). You will also need the payment structure. Most of the time it will be monthly, but bimonthly and biweekly payment structures may be available.

2. Determine the number of payments per year. Monthly plans have 12 payments per year and bimonthly plans have 24. Biweekly plans have 26, since there are 52 weeks in a year and payments occur every two weeks.

3. Calculate the total number of payments and the interest rate for each payment period. For the number of payments, multiply the number of payments per year by the term. For the interest rate, divide the APR by the number of payments per year. For example, for a 30-year FRM at 6 percent APR with monthly payments, the number of payments would be 30 x 12 = 360. and the interest rate would be 0.06 / 12 = 0.005

4. Use the per payment values to calculate the payment. The formula is:

   P = L[c(1 + c)^n]/[(1 + c)^n - 1]

   P = Payment amount
   L = Loan amount
   c = per payment interest rate
   n = number of payments

   For a $200,000, 30-year FRM at 6 percent with monthly payments:

   P = 200000[0.005(1 + 0.005)^360]/[(1 + 0.005)^360 - 1]
   P = $1,199.10

Amortization

1. Calculate the interest and principal portions of the first payment. Multiply the per-payment interest rate by the loan amount to get the interest and subtract the interest from the payment amount to get the principal.

   200000 x 0.005 = $1,000 interest
   1199.10 - 1000 = $1,199.10 principal

2. Subtract the principal from the loan amount to get the loan balance.

   200000 - 199.10 = $199,800.90

3. Repeat the process, using the new loan balance from each new calculation as the loan amount. Continue until the loan amount has been reduced to zero. The second iteration of this example is:

   199800.90 x 0.005 = $999.00 interest
   1199.10 - 999 = $200.10 principal
   199800.90 - 200.10 = $199,600.90 new loan value

Tips & Warnings

• Many spreadsheets have built-in function to calculate the loan payment, and by entering the formulas and copying the cells, the amortization is greatly simplified.

References

• The Mortgage Professor: Formulas
• The Mortgage Professor: FRMs