If the quoted rate for a short term loan is 28.79% APR, and interest is compounded continuously, what is the effective interest rate per quarter and the effective annual interest rate

The effective Annual interest rate is 32.05%

The effective interest rate per quarter is 8.01%

Explanation:

The effective interest rate is the interest rate adjusted to the nominal interest rate by the compounding or periods of an interest rate so in this case the nominal interest rate is 28.79% which is the annual percentage rate so we will calculate the annual effective interest rate by the following formula:

ieff = (1+inom/n) ^n

where we substitute the above mentioned nominal interest rate 28.79% which is inom.

n represents the periodic payments which is 4 here as we are told the compounding happens per quarter. then we will substitute on the above mentioned formula to get ieff which is the effective interest rate.

ieff = (1+28.79%/4) ^4

ieff = 32.05% which is the effective annual interest rate

then the effective interest rate per quarter is 32.05%/4 = 8.01% as that is the annual interest rate adjusted to per quarter.