CFA Level I · CFA Level I Exam · The Time Value of Money in Finance
A bank advertises a loan at a stated annual rate of 12% compounded monthly. An analyst compares it with a competing loan with 12.5% compounded semiannually. On an effective annual rate basis, the first loan's rate is closest to, and relative to the second loan is most likely:
The monthly-compounded loan has an effective annual rate of about 12.68%, from 1.01 to the twelfth power minus one. The second loan's rate is about 12.89%, from 1.0625 squared minus one, so the first loan is cheaper on an effective basis.
- A12.68%, lower than the second loanCorrect
- B12.68%, higher than the second loan
- C12.00%, lower than the second loan
Explanation
First EAR = (1.01)^12 − 1 = 12.68%. Second EAR = (1 + 0.0625)^2 − 1 = 1.12891 − 1 = 12.89%. So the first is lower. Claiming higher ignores the second loan's compounding; 12.00% ignores compounding altogether.
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