Question
Calculate the amount and cornpound interest for the following, when cornpounded annually:
$Rs.7,500$ for $2 \frac{1}{2}$ years ; $r=16 \%$ p.a.
$Rs.7,500$ for $2 \frac{1}{2}$ years ; $r=16 \%$ p.a.
✓
Answer
$P=\operatorname{Rs} 7,500 ; t=2 \frac{1}{2} \text { years } ; r=16 \% \text { p.a. } $
$A=P\left(1+\frac{r}{100}\right)^n$
$ A=\operatorname{Rs} 7500\left(1+\frac{16}{100}\right)^2\left(1+\frac{16}{100}\right)^{\frac{1}{2}} $
$=\operatorname{Rs} 7500 \times 1.16 \times 1.16 \times\left(1+\frac{1}{2} \times \frac{16}{100}\right) $
$=\text { Rs } 7,500 \times 1.16 \times 1.16 \times 1.08 $
$ =\text { Rs } 10,899.36 \\ \text { C.I. }=A-P$
$ =\text { Rs }(10,899.36-7,500) $
$=\text { Rs } 3,399.36 $
Hence, Amount $= Rs.10,899.36$ and C.I. $=Rs.3,399.36$
$A=P\left(1+\frac{r}{100}\right)^n$
$ A=\operatorname{Rs} 7500\left(1+\frac{16}{100}\right)^2\left(1+\frac{16}{100}\right)^{\frac{1}{2}} $
$=\operatorname{Rs} 7500 \times 1.16 \times 1.16 \times\left(1+\frac{1}{2} \times \frac{16}{100}\right) $
$=\text { Rs } 7,500 \times 1.16 \times 1.16 \times 1.08 $
$ =\text { Rs } 10,899.36 \\ \text { C.I. }=A-P$
$ =\text { Rs }(10,899.36-7,500) $
$=\text { Rs } 3,399.36 $
Hence, Amount $= Rs.10,899.36$ and C.I. $=Rs.3,399.36$
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