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CA Foundation · Quantitative Aptitude · Mathematics of Finance

Which nominal rate per annum, compounded half-yearly, is equivalent to an effective annual rate of 21%?

The nominal rate is 20% per annum compounded half-yearly. Setting (1+r)^2 = 1.21 gives r = 10% per half-year, and doubling it gives the annual nominal rate of 20%, which yields an effective rate of 21%.

  1. A20%Correct
  2. B21%
  3. C10%
  4. D19.5%

Explanation

Let the half-yearly rate be r. Then (1+r)^2 = 1.21, so 1+r = 1.10 and r = 10% per half-year. Nominal annual rate = 2 x 10 = 20%. The 10% option is the half-yearly rate, not the nominal annual rate.

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