Compute the compound interest on Rs.1000 for 2 years at 10% per annum when compounded half yearly. (write answer in the nearest integer).

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Solution

Here, Principal P = Rs. 1000
R $= 10 %$ per annum and $n = 2$ years
$∴$ Amount after 2 years = P ${(1 + \frac{R}{200})}^{2 n}$
= Rs. $1000 \times {(1 + \frac{10}{200})}^{2 \times 2} = R s .1000 \times {(1 + \frac{1}{20})}^{4} = R s .1000 \times$ ${(\frac{21}{20})}^{4}$
= $R s .1000 \times \frac{21}{20} \times \frac{21}{20} \times \frac{21}{20} \times \frac{21}{20} = R s .1215 .50$
Hence, compound interest = Amount - Principal
$= R s . 1215.50 - R s . 1000 = R s . 215.50$

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