Question

Which of the following APRs compounded monthly is equivalent to an APR of 15.15% compounded quarterly using 360-day calendar years, 30-day months, and 3-month quarters?

Answer 1

Annual Interest Rate = 15.15% compounded quarterly

Quarterly Interest Rate = 15.15% / 4
Quarterly Interest Rate = 3.7875%

Effective Annual Rate = (1 + Quarterly Interest Rate)^4 - 1
Effective Annual Rate = (1 + 0.037875)^4 - 1
Effective Annual Rate = 1.1603265 - 1
Effective Annual Rate = 0.1603265 or 16.03265%

Monthly Interest Rate = (1 + Effective Annual Rate)^(1/12) - 1
Monthly Interest Rate = (1 + 0.1603265)^(1/12) - 1
Monthly Interest Rate = 1.012469 - 1
Monthly Interest Rate = 0.012469 or 1.2469%

Annual Interest Rate = 12 * Monthly Interest Rate
Annual Interest Rate = 12 * 1.2469%
Annual Interest Rate = 14.96% compounded monthly