# What is the fixed rate mortgage formula?

Answer:
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.

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