Question

Which of the following APRs compounded quarterly is equivalent to an APR of 8.65% compounded daily using 360-day calendar years, 30-day months, and 3-month quarters?

a) 8.087%

b) 8.306%

c) 8.525%

d) 8.743%

e) 8.962%

Answer 1

- APR compounded daily = 8.65%

Calculating its Effective Annual Rate(EAR):-

where, r = APR = 8.65%

m = no of times compounding in a year = 360

EAR = 9.0340194%

APR compounded Quarterly is equal to APR compounded daily which means that EAR of both will be the same.

Now, Calculating APR of compounded Quarterly using EAR:-

where, r = APR

m = no of times compounding in a year = 4

EAR = 0.090340194

Taking 4-root on both sides,

1.0218579 = 1+ r/4

0.0218579 = r/4

r = 8.743%

Hence, APR is 8.743% compounded Quarterly.

Option D