CFA Level IQuantitative MethodsMedium
A bank advertises a stated annual interest rate of 8%, compounded quarterly. What is the effective annual rate (EAR)?
- A8.30%
- B8.16%
- C8.24%
- D8.00%
Show answer & explanationAnswer & explanation
Correct answer: C. 8.24%
EAR = (1 + 0.08/4)^4 - 1 = (1.02)^4 - 1 = 1.08243216 - 1 = 8.24%. The more frequent the compounding, the greater the EAR relative to the stated rate.
Why the other options are wrong
- A. This overstates the effect of compounding beyond the actual quarterly result.
- B. This corresponds to semiannual compounding, not quarterly.
- D. This ignores compounding entirely, equal to the stated rate.
Effective Annual Rate (EAR)
EAR converts a stated (nominal) annual rate compounded m times per year into an equivalent annual rate reflecting the effect of compounding.
- EAR = (1 + periodic rate)^m - 1
- EAR > stated rate whenever m > 1
- EAR increases as compounding frequency increases
Memory trick: More compounding, more compounding power.