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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Time Value of Money and Annuity - Simple and Compound Interest

A finance company wants an effective annual rate of 21% on a loan where interest is compounded half-yearly. Given that (1.10)^2 = 1.21, what nominal annual rate must it quote?

The company must quote a nominal 20% per annum compounded half-yearly. Since the effective rate is 21%, (1+r)^2 equals 1.21, so the half-yearly rate is 10%. Doubling it for two periods per year gives the nominal annual rate of 20%.

  1. A10%
  2. B20%Correct
  3. C21%
  4. D20.5%

Explanation

Let the half-yearly rate be r. (1+r)^2 = 1.21, so 1+r = 1.10 and r = 10% per half-year. Nominal annual rate = 2 x 10% = 20%. Quoting 10% confuses the half-yearly rate with the annual one.

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