Question : What is the compound interest on INR 10000 in 1 year 6 months at 10% per annum, the interest being compounded half-yearly?
Option 1: INR 1625.50
Option 2: INR 1576.25
Option 3: INR 1826.50
Option 4: INR 1422.25
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Correct Answer: INR 1576.25
Solution : Rate, $R$ = 10% Term, $n$ = 1 year Principal sum, $P$ = INR 10000 When compounded half-yearly, Amount = $P(1+\frac{R}{200})^{2n}$ Compound interest = $P(1+\frac{R}{200})^{2n}-P$ = $10000(1+\frac{10}{200})^{2×1.5}-10000$ = $10000(1+\frac{1}{20})^{3}-10000$ = $10000(\frac{21}{20})^{3}-10000$ = $10000(\frac{21^3}{20^3}-1)$ = $10000(\frac{21^3-20^3}{8000})$ = $\frac{10000×(441+400+420)×1}{8000}$ = $\frac{12610}{8}$ = INR $1576.25$ Hence, the correct answer is INR 1576.25.
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