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CA Foundation · Quantitative Aptitude · Mathematics of Finance

A bank wants the effective annual rate on a deposit to be 21% when interest is compounded half-yearly. What nominal annual rate must it quote?

The nominal rate must be 20% per annum. Setting (1 + i)^2 = 1.21 gives 1 + i = 1.1, so the half-yearly rate is 10%. Doubling it gives the nominal annual rate of 20%, which checks back to an effective rate of 21%.

  1. A18%
  2. B19%
  3. C20%Correct
  4. D21%

Explanation

Let the half-yearly rate be i. Then (1+i)^2 = 1.21, so 1+i = 1.1 and i = 10% per half-year. Nominal rate = 2 × 10% = 20%. Check: (1.10)^2 - 1 = 21%. Quoting 21% nominal would give an effective rate above 21%.

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