Question
Mohan invested a certain sum at compound interest, compounded annually. If the interests for two successive years were $Rs.600 $ and $Rs.648,$ calculate the rate of interest and the sum invested.
✓
Answer
For the second year:
$ A=R s 648 ; P=R s 600 ; n=1 ; r=?$
$\therefore A=P\left(1+\frac{r}{100}\right)^n$
$\Rightarrow 648=600\left(1+\frac{r}{100}\right)^1$
$\Rightarrow 648=600+6 r$
$\Rightarrow 6 r=48$
$\Rightarrow r=8 $
Hence, rate of interest $=8 \%$
For the first year:
$ I=R s 600 ; r=8 \% ; n=1 ; P=?$
$I=\frac{P \times r \times n}{100}$
$\text { Rs } 600=\operatorname{Rs} \frac{P \times 8 \times 1}{100}$
$P=\operatorname{Rs} \frac{60000}{8}$
$P=\text { Rs } 7,500 $
The sum invested $= Rs.7,500.$
$ A=R s 648 ; P=R s 600 ; n=1 ; r=?$
$\therefore A=P\left(1+\frac{r}{100}\right)^n$
$\Rightarrow 648=600\left(1+\frac{r}{100}\right)^1$
$\Rightarrow 648=600+6 r$
$\Rightarrow 6 r=48$
$\Rightarrow r=8 $
Hence, rate of interest $=8 \%$
For the first year:
$ I=R s 600 ; r=8 \% ; n=1 ; P=?$
$I=\frac{P \times r \times n}{100}$
$\text { Rs } 600=\operatorname{Rs} \frac{P \times 8 \times 1}{100}$
$P=\operatorname{Rs} \frac{60000}{8}$
$P=\text { Rs } 7,500 $
The sum invested $= Rs.7,500.$
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