Question

Which of the following APRs compounded quarterly is equivalent to an APR of 8.15% compounded daily using 360-day calendar years, 30-day months, and 3-month quarters? 7.821% 8.027% 8.233% 8.438% 8.644%

Answer 1

For two different compounding times their value will be equal when their effective annual rate equals

Effective annual rate formula

= (1+r/n)^nt -1

Where n is no of compounding periods

r is rate of interest

Apr 8.15 compounded daily

= (1+0.0815/360)^360 - 1 =8.49%

Now we will calculate effective annual rate for quarterly compounding

= (1+x/4)^4 -1 = 8.49%

By substituting option in the above equation we get x as 8.233%

This also can be solved by using mathmatical equation

= (1+x/4)= (0.0849)^1/4

We get x as 0.08233