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6.Interest
hard
An amount of money at compound interest grows up to $Rs. 3840$ in $4$ $years$ and up to $Rs. 3936$ in $5$ $years$. Find the rate of interest (In $\%$) ?
A
$2.5$
B
$2$
C
$3.5$
D
$2.05$
Solution
$A=P\left(1+\frac{r}{100}\right)^{t}$
$3840=P\left(1+\frac{r}{100}\right)^{4}$
$3936=P\left(1+\frac{r}{100}\right)^{5}$
On dividing Eq. (ii) by Eq. (i), we get
$\frac{3936}{3840}=1+\frac{ r }{100} \Rightarrow \frac{3936}{3840}-1=\frac{ r }{100}$
$\Rightarrow \frac{3936-3840}{3840}=\frac{ r }{100}$
$\Rightarrow \frac{96}{3840}=\frac{r}{100} \Rightarrow r=\frac{96 \times 100}{3840}$
$\therefore \quad r =2.5 \%$ per annum
Standard 13
Quantitative Aptitude
