Question

Find the APR, or stated rate, for an effective rate (EAR) of 12.7 percent compounded monthly. (Enter your answer as a percentage, omit the "%" sign in your response, and round your answer to 2 decimal places. For example, 0.12345 or 12.345% should be entered as 12.35.)

Answer 1

We can use the following formula to calculate the annual percentage rate:
APR=T*[((1+EAR)^1/T)-1]
Where,
APR is annual percentage rate
EAR is effective rate.
T is given as the number of times the rate of interest is compounded in a year.
Given that,
Effective Annual Rate (EAR)= 12.7%
It is given that, EAR of 12.7% is compounded monthly. Hence, with monthly compounding, the interest rate compounds 12 times in a year.
APR=T*[((1+EAR)^1/T)-1]
Substituting the values in the above equation, we get:
APR=12*[((1+12.7%)^1/12)-1]
=12*[((1.127)^1/12)-1]
=12*(1.01001-1)
=12*.01001=0.12012 or 12.01% (rounded upto 2 decimal places)
So, annual percentage rate (APR) is 12.01 percent.