CFA Level I · CFA Level I Exam · The Time Value of Money in Finance
A lender offers a loan at a 5.00% stated annual rate compounded quarterly. A borrower wants a rate with semiannual compounding that is equivalent in effective annual terms. The equivalent stated annual rate is closest to:
The equivalent semiannually compounded stated rate is about 5.03%. First convert 5% quarterly compounding to an effective annual rate of about 5.09%, then take the square root of 1.0509 minus one and double it. Fewer compounding periods require a slightly higher stated rate.
- A4.97%
- B5.03%Correct
- C5.06%
Explanation
EAR = (1.0125)^4 − 1 = 1.050945 − 1 = 5.0945%. Semiannual rate = (1.050945)^(1/2) − 1 = 0.025157 (1.025157^2 = 1.050945). Stated rate = 2 × 2.5157% = 5.03%. The 4.97% figure results from adjusting in the wrong direction; 5.06% comes from taking the EAR as a stated rate and rounding up.
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