Question
Calculate the amount and the compound interest for the following, when cornpounded half-yearly:
$Rs.6,000$ for $1 \frac{1}{2}$ years at $10 \%$ p.a.

Answer

$Rs.6,000$ for $1 \frac{1}{2}$ years at $10 \%$ p.a.
$P=Rs.6,000 ; t=1 \frac{1}{2}$ years $; r=10 \%$ p.a. $=5 \%$
half-yearly.
$A=P\left(1+\frac{r}{100}\right)^n$
$A=\operatorname{Rs} 6000\left(1+\frac{5}{100}\right)^2\left(1+\frac{10}{100}\right)^{\frac{1}{2}}$
$=\text { Rs } 6000 \times 1.05 \times 1.05 \times\left(1+\frac{1}{2} \times \frac{10}{100}\right)$
$=\text { Rs } 61000 \times 1.05 \times 1.05 \times 1.05$
$=\text { Rs } 6945.75$
$\text { C.I. }=A-P$
$=\text { Rs }(6,945.75-6,000)$
$=\text { Rs } 945.75$
Hence, Amount $= Rs.6,945.75$ and C.I. $=Rs.945.75$

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