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FRM Part I · FRM Exam Part I · Properties of Interest Rates

An investor deposits 1,000,000 at a rate of 4% per annum compounded continuously for 2 years. A second bank offers a rate compounded semiannually that gives exactly the same terminal value after 2 years. Which is closest to the semiannual rate?

The semiannual rate is about 4.04%. Matching terminal values requires (1 + R/2) to equal e raised to 0.02, which is 1.0202, so R equals 4.04%. Discrete compounding needs a higher nominal rate than continuous compounding to give equal growth.

  1. A3.96%
  2. B4.00%
  3. C4.04%Correct
  4. D4.08%

Explanation

Terminal value factor over 2 years is e^0.08. Need (1+R/2)^4 = e^0.08, so 1+R/2 = e^0.02 = 1.020201 and R = 4.04%. The 3.96% answer mistakenly takes the opposite direction of the conversion.

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