What is the fixed rate mortgage formula?


The fixed rate mortgage formula demonstrates that the mortgage monthly payment is calculated over a fixed period, so that the loan is fully amortized in the end and the fixed rate mortgage balance is zeroed.

The most commonly used fixed rate mortgage formula is

monthly fixed mortgage payment = (r / (1 - (1 + r)- N))P,

  • r is the monthly fixed rate expressed with a fraction - if annual interest rate is 7 percent, r will be 7 divided by 100 divided by 12;
  • N is the number of monthly payments needed to amortize the fixed rate loan – if your mortgage loan is taken over 10 years, N will be 10*12=120;
  • and P is the amount of principal.

For example: a $150,000 fixed rate mortgage taken over 15 years with annual rate of 5.85 will result in the following calculations based on the above fixed rate mortgage formula:

monthly fixed mortgage payment =
= ((5.85/100/12)/(1-(1+5.85/100/12)^(-15*12)))*150000

In other words, for this example the monthly payment will be $1253.66.

Calculating by substitution in the fixed rate mortgage formula will get you there; so will substituting in an online calculator for fixed rate mortgages.

Mortgage rates hit their lowest since 1955. Ask the home loan experts we recommend Quicken Loans how to take advantage of them.
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