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

Mr. Sharma wants an effective annual rate of exactly 21% from a deposit that is compounded twice a year. What nominal annual rate (compounded half-yearly) must the bank offer?

The bank must offer a nominal rate of 20% per annum compounded half-yearly. Since the square of one plus the half-yearly rate must equal 1.21, the half-yearly rate is 10%, and doubling it gives the nominal annual rate of 20%.

  1. A10%
  2. B20%Correct
  3. C21%
  4. D10.5%

Explanation

Let the half-yearly rate be r. Then (1+r)^2 = 1.21, so 1+r = 1.1 and r = 10% per half-year. Nominal annual rate = 2 x 10% = 20%. Check: 1.1^2 = 1.21. Option 10% is only the half-yearly rate, not the annual nominal rate.

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