CFA Level I · CFA Level I Exam · The Time Value of Money in Finance
A bank quotes a loan at a stated annual rate of 6.00% compounded monthly. The effective annual rate is closest to:
The effective annual rate is about 6.17%. Monthly compounding at 0.5% per month gives 1.005 raised to the 12th power, about 1.0617. The stated 6.00% understates the true annual cost because interest earns interest within the year.
- A6.00%
- B6.17%Correct
- C6.45%
Explanation
EAR = (1 + 0.06/12)^12 − 1 = 1.005^12 − 1 = 1.061678 − 1 = 6.17%. The 6.00% option ignores intra-year compounding. The 6.45% option would result from compounding at a rate that is too high, such as using daily or continuous compounding on a larger rate.
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