Calculate the amount and cornpound interest for the following, wh… - Vidyadip

Question

Calculate the amount and cornpound interest for the following, when cornpounded annually:
$Rs.8,000$ for $1 \frac{1}{2}$ years at $12 \%$ p.a.

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Answer

$P=\operatorname{Rs} 8,000 ; t=1 \frac{1}{2} \text { years } ; r=12 \% \text { p.a. }$
$ A=P\left(1+\frac{r}{100}\right)^{ n } $
$ A=\operatorname{Rs} 8000\left(1+\frac{12}{100}\right)\left(1+\frac{12}{100}\right)^{\frac{1}{2}}$
$=\text { Rs } 8000 \times 1.12 \times\left(1+\frac{1}{2} \times \frac{12}{100}\right) $
$=\text { Rs } 8,000 \times 1.12 \times 1.06$
$=\text { Rs } 9,497.60$
$ \text { C.I. }=\text { A }-P$
$=\operatorname{Rs}(9,497.60-8,000) $
$=\operatorname{Rs~} 1,497.60$
Hence, Amount $= Rs.9,497.60$ and C.I. $=Rs.1,497.60$

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