Question

Which of the following APRs compounded monthly is equivalent to an APR of 13.65% compounded quarterly using 360-day calendar years, 30-day months, and 3-month quarters?

Answer 1

Answer-

Given

APR compounded quarterly = 13.65 %

( 1 + (APR compounded monthly / 3) )³   - 1 = 13.65 % [ As one quarter has 3 months - / 3 - number of ccompounding periods ]

( 1 + (APR compounded monthly / 3) )³ - 1 = 0.1365

( 1 + (APR compounded monthly / 3) )³ = 1 + 0.1365

( 1 + (APR compounded monthly / 3) )³ = 1.1365

( 1 + (APR compounded monthly / 3) = 1.1365^1/3

( 1 + (APR compounded monthly / 3) = 1.043529

APR compounded monthly / 3 = 1.043529 - 1

APR compounded monthly / 3 = 043529

APR compounded monthly =.043529 x 3

APR compounded monthly = 0.130587

APR compounded monthly = 13.0587 %