What is the formula for annual percentage rate (APR)?


The annual percentage rate (APR) is easy to calculate when the lender has disclosed all loan related costs. To calculate APR, you will simply need to know the closing costs, interest rate, loan amount and mortgage amortization period and substitute in the formula for annual percentage rate (APR).

The APR of a true no-cost loan will coincide with the advertised interest rate. The APR of a fixed rate loan is greater than the interest rate, and the APR of an adjustable rate mortgage sometimes is lower than the quoted rate.

Consider the following example:

You are borrowing $200,000
At interest rate 6.25%
For period of 15 years
Closing costs $4,800

Your APR is 6.625%, if the mortgage loan is a fixed rate. Calculating the APR of adjustable rate mortgages is an altogether different matter.

How to arrive at my annual percentage rate (APR) and what is the formula?

APR is the most important aspect when comparing credit cards and mortgage loan terms. The easiest way to approach to arrive at the APR of an advertised product is to use web APR calculators. Remember that you should only compare loans with the same maturities.

There are 4 methods and formulae used by lenders to calculate your APR:

  • Actuarial method
  • Constant-ratio method
  • N-ratio method
  • Direct-ratio method

The actuarial method and formula for annual percentage rate (APR) are the most widely used by lenders to calculate APR. Detailed formulae, examples and explanations for borrowers of the actuarial method are provided in Regulation Z in the Consumer Credit Protection Act.

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