Question : What is the effective annual rate of interest corresponding to a nominal rate of 10% per annum payable half-yearly?
Option 1: 10.25%
Option 2: 12.75%
Option 3: 9.25%
Option 4: 11.50%
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Correct Answer: 10.25%
Solution : Rate, $\frac{R}{2}$ = 10% Time, $n$ = 1 year Let principal sum, $P$ be INR 100. When compounded half-yearly, Amount = $P(1+\frac{\frac{R}{2}}{200})^{2n}$ = $100(1+\frac{10}{200})^{2}$ = $100(\frac{21}{20})^{2}$ = $\frac{441}{4}$ = INR 110.25 Effective rate = $\frac{110.25-100}{100}×100$ = 10.25% Hence, the correct answer is 10.25%
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