CA Foundation · Quantitative Aptitude · Mathematics of Finance
A bank offers a nominal rate of 12% per annum compounded quarterly. What is the effective annual rate of interest, correct to two decimal places?
The effective annual rate is 12.55%. With quarterly compounding the periodic rate is 3% and there are four periods, so (1.03)^4 - 1 equals about 0.1255. This exceeds the nominal 12% because interest is earned on interest within the year.
- A12.00%
- B12.36%
- C12.55%Correct
- D12.68%
Explanation
Quarterly rate = 12/4 = 3%. Effective rate = (1.03)^4 - 1 = 1.12550881 - 1 = 12.55%. The option 12.36% is the effective rate for half-yearly compounding (1.06^2 - 1), which uses the wrong compounding frequency.
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