CMA Foundation · Fundamentals of Business Mathematics and Statistics · Time Value of Money and Annuity - Simple and Compound Interest
A bank quotes a nominal rate of 12% per annum compounded half-yearly. What is the effective annual rate of interest?
The effective annual rate is 12.36%. A nominal 12% compounded half-yearly gives 6% per half-year, and compounding twice gives (1.06)^2 - 1 = 0.1236. Hence the effective rate is slightly above the nominal rate because interest is earned on interest.
- A12.00%
- B12.36%Correct
- C12.55%
- D13.20%
Explanation
Half-yearly rate = 6%. Effective rate = (1.06)^2 - 1 = 1.1236 - 1 = 0.1236, i.e. 12.36%. The 12.55% option comes from compounding quarterly (1.03^4), which does not match half-yearly compounding.
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