CA Foundation · Quantitative Aptitude · Mathematics of Finance
A sum is invested at 8% per annum compounded quarterly. Which expression gives the effective annual rate of interest?
The effective annual rate is (1.02)^4 - 1. The nominal 8% is divided by four quarters to get 2% per quarter, and compounding over four quarters in a year gives (1.02)^4, from which 1 is subtracted to isolate the interest rate.
- A(1.08)^4 - 1
- B(1.02)^4 - 1Correct
- C(1.04)^2 - 1
- D(1.02)^8 - 1
Explanation
Quarterly rate = 8/4 = 2% = 0.02, with 4 quarters per year. Effective rate = (1 + 0.02)^4 - 1. The option (1.08)^4 - 1 wrongly applies the annual rate in each quarter.
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