APR and EAR

In the previous section's example, we mentioned that "10% compounded semiannually" is equivalent to "10.25% per year". In the finance world, here the 10% is called Annual Percentage Rate (APR) and 10.25% is called Effective Annual Rate (EAR). Although EAR is the real interest rate (so you can compare apple with apple), APR is the interest rate what the lenders are required to quote you. That is to say, it is crucial to know how to convert between EAR and APR, especially when it comes to applying for loans and mortgages.

Before we start our example on the conversion between EAR and APR, let's give a formal formula of APR first.

APR = (return per period) × (number of periods within a year)

In our previous example, the period is 6 months, so we have 5% per period and 2 periods within in a year:

APR = (return per period) × (number of periods within a year)

= 5% × 2

= 10%

That is indeed what we have.

We then plug APR = 60% and m = 2 into this equation.