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
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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