CA Foundation · Quantitative Aptitude · Mathematics of Finance
A finance company advertises a deposit scheme with interest compounded half-yearly and an effective annual rate of 10.25%. What is the nominal annual rate of interest?
The nominal rate is 10% per annum. Since (1+r)^2 equals 1.1025, the half-yearly rate r is 5%. Doubling this for the two half-years in a year gives the nominal annual rate of 10%, which compounds to an effective 10.25%.
- A10.00%Correct
- B10.25%
- C9.75%
- D5.00%
Explanation
Let the half-yearly rate be r. Then (1+r)^2 = 1.1025, so 1+r = 1.05 and r = 5% per half-year. Nominal annual rate = 2 x 5 = 10%. The option 5% is only the half-yearly rate, not the annual nominal rate.
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