# Find the APR, or stated rate, in each of the following cases. Stated Rate (APR) Number of Times...

## Question:

Find the APR, or stated rate, in each of the following cases.

 Stated Rate (APR) Number of Times Compounded Effective Rate (EAR) % Semiannually 15.25% % Monthly 11.25 % Weekly 9.75 % Daily 7.75

## APR and EAR:

APR or annual percentage rate is the stated rate of return which is divided as per the number of periods in a year to find out the periodic rate. EAR or effective annual rate is the annualized effective rate of the stated APR.

We will apply the EAR formula in all the cases to find out the APR

EAR = (1 + APR / n)^n - 1

Here,

EAR = Effective Annual Rate

APR = Annual percentage rate

n = Number of periods in a year, for example, 2 for semi annual, 12 for monthly, 52 for weeks and 365 for days.

Case 1:

0.1525 = (1 + APR / 2)^2 - 1

or,

APR = 14.71%

Case 2:

0.1125 = (1 + APR / 12)^12 - 1

or,

APR = 10.71%

Case 3:

0.0975 = (1 + APR / 52)^52 - 1

or,

APR = 9.31%

Case 4:

0.0775 = (1 + APR / 365)^365 - 1

or,

APR = 7.47%