APR and EAR

APR

APR stands for Annual Percentage Rate. It is sometimes simply referred to as rate.

It measures the amount of Simple Interest earned in a year. (Simple Interest is the interest earned without compounding).

Many banks quote interest rates in terms of APR. However, APR is not the interest that we actually earn/pay. Therefore, APR is not a discount rate.

APY / EAR

APY (Annual Percentage Yield) or EAR (Effective Annual Rate) measures the actual amount of interest earned/paid in a year.

It is the discount rate used while calculating interest and discounting cash flows.

APR can be used to compute EAR:

$EAR = (1+\frac{APR}{k})^k - 1 = (1+i)^k - 1$

where:

k: the number of compounding periods per year

• k=12 if compounded monthly

• k=2 if compounded semi-annually

• k=365 if compounded daily (or 360 or 252 business days depending on the terms of the institution)

i: periodic interest rate (or) periodic discount rate i.e. $\frac{APR}{k}$

Simple Example

If you invest $100 in a CD (Certificate of Deposit) offering 5% APR compounded semi-annually,
how much money will you have in one year?

$EAR = (1+\frac{0.05}{2})^2 - 1 = 0.0506$

So, amount after one year = 100*(1+0.0506) = $105.06

Note: if you discount cash flows using EAR, then measure time in years. If you discount cash flows using the periodic interest rate, then measure time in periods.