Question

Which of the following APRs compounded monthly is equivalent to an APR of 14.15% compounded quarterly using 360-day calendar years, 30-day months, and 3-month quarters?

	12.960%
	13.320%
	13.680%
	14.040%
	14.400%

Answer 1

Quarterly compounding=((1+r/n)^n)-1

r=interest rate

n=number of periods=4 (4 quarters in a quarter)

Quarterly compounding=((1+(14.15%/4))^4)-1=14.92%

Now check the each option below by compounding monthly

i) Monthly compounding=((1+(12.96%/12))^12)-1=13.76%

ii) Monthly compounding=((1+(13.32%/12))^12)-1=14.16%

iii) Monthly compounding=((1+(13.68%/12))^12)-1=14.57%

iv) Monthly compounding=((1+(14.04%/12))^12)-1=14.98%

Option iv is almost equal to quarterly compounding value