CFA Level I · CFA Level I Exam · The Time Value of Money in Finance
An investment offers an effective annual rate of 8.24%. The equivalent stated annual rate with semiannual compounding is closest to:
The equivalent stated rate is about 8.08%, which is closest to 8.12%. Take the square root of 1.0824 to get a semiannual periodic rate of roughly 4.04%, then multiply by two periods per year to obtain the stated annual rate.
- A7.92%
- B8.00%Correct
- C8.12%
Explanation
Semiannual periodic rate = (1.0824)^(1/2) - 1 = 1.04 - 1 = 4.00%, since 1.04^2 = 1.0816... checking: 1.04^2 = 1.0816 gives 8.16%; so 1.0824^(0.5) = 1.04038, about 4.04%... stated rate = 2 x 4.04% = 8.08%, closest to 8.00%? Compared with 7.92% and 8.12%, 8.08% is nearest to 8.12%.
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