CA Foundation · Quantitative Aptitude · Mathematics of Finance
A deposit earns interest at a nominal rate of 10% per annum, compounded half-yearly. What is the effective annual rate of interest?
The effective annual rate is 10.25%. A nominal 10% compounded half-yearly means 5% per half-year, so each rupee grows to (1.05)^2 = 1.1025 in one year. The gain of 0.1025 per rupee is 10.25%, which exceeds the nominal rate because interest is earned on previously credited interest.
- A10.00%
- B10.25%Correct
- C10.50%
- D20.25%
Explanation
The half-yearly rate is 10%/2 = 5%. Growth factor for one year = (1.05)^2 = 1.1025, so the effective rate = 0.1025 = 10.25%. The option 10.00% ignores the extra interest earned on interest within the year.
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