Question : INR 20,000 is lent at compound interest at an annual rate of 16% for 1 year. If the compounding of interest is done half yearly, then how much interest will be obtained?
Option 1: INR 3180
Option 2: INR 3396
Option 3: INR 3224
Option 4: INR 3328
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Correct Answer: INR 3328
Solution :
Rate, $R$ = 16%
Tem, $n$ = 1 year
Principal sum, $P$ = INR 20000
When compounded half-yearly,
Amount = $P(1+\frac{R}{200})^{2n}$
Compound interest = $P(1+\frac{R}{200})^{2n}-P$
= $20000(1+\frac{16}{200})^{2}-20000$
= $20000(1+\frac{2}{25})^{2}-20000$
= $20000(\frac{27}{25})^{2}-20000$
= $20000(\frac{27^2}{25^2}-1)$
= $20000(\frac{27^2-25^2}{625})$
= $\frac{20000×52×2}{625}$
= INR 3328
Hence, the correct answer is INR 3328.
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