CA Foundation · Quantitative Aptitude · Mathematics of Finance
A nominal rate of 8% per annum is compounded half-yearly. The effective annual rate is r%. What is the value of r?
The effective rate is 8.16%. Half-yearly compounding at 8% nominal means 4% each half-year. Squaring 1.04 gives 1.0816, so after removing the principal the effective annual rate is 8.16%, which exceeds the nominal 8% because of compounding.
- A8.00
- B8.16Correct
- C8.24
- D8.32
Explanation
Half-yearly rate = 4%. Effective rate = (1.04)^2 - 1 = 1.0816 - 1 = 0.0816, i.e. 8.16%. The figure 8.24% results from wrongly using 4.04% type rounding and 8.32% from adding 4% twice plus extra; neither matches the calculation.
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