FRM Part I · FRM Exam Part I · Pricing Conventions, Discounting, and Arbitrage
A deposit pays a stated annual rate of 6% compounded semiannually. What is the effective annual rate (EAR)?
The effective annual rate is 6.09%. With semiannual compounding each half-year earns 3%, so the year-end growth factor is 1.03 squared, or 1.0609. The stated 6% understates the true annual yield because interest earned in the first half-year itself earns interest.
- A6.00%
- B6.09%Correct
- C6.14%
- D6.18%
Explanation
Semiannual compounding gives (1 + 0.06/2)^2 - 1 = 1.03^2 - 1 = 6.09%. The 6.00% answer ignores compounding. The 6.14% answer assumes quarterly compounding. The 6.18% answer assumes continuous compounding (e^0.06 - 1).
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