FRM Part I · FRM Exam Part I · Properties of Interest Rates
A bank quotes a nominal annual rate of 8% compounded quarterly. What is the equivalent annual effective rate, to the nearest 0.01%?
The effective annual rate is 8.24%. A quarterly rate of 2% compounded four times gives 1.02 to the fourth power, which is 1.0824, so the effective annual rate is 8.24%. Simply quoting the nominal 8% ignores the extra interest earned from compounding within the year.
- A8.00%
- B8.24%Correct
- C8.32%
- D8.16%
Explanation
Quarterly rate is 8%/4 = 2%. Effective annual rate = (1.02)^4 - 1 = 1.08243 - 1 = 8.24%. The 8.32% option is the semiannual-style or monthly-style mistake: 8.32% is roughly the effective rate under monthly or continuous compounding, not quarterly.
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