Question

A sum of $Rs.1728$ becomes $Rs.3375$ in $3$ years at compound interest, compound annually. Find the rate of interest.

• A. $10\%$
• B. $15\%$
• C. $20\%$
• D. $25\%$

Answer 1

The correct option is D $25\%$

Given: $P=Rs.1728,A=Rs.3375,n=3$ years

We need to find rate of interest i.e. $r\%$
$A=P\left[{(1+\frac{r}{100})}^n\right]$
$\Rightarrow 3375=1728\left[{(1+\frac{r}{100})}^3\right]$
$\Rightarrow \frac{3375}{1728}={(1+\frac{r}{100})}^3$
$\Rightarrow {\left(\frac{15}{12}\right)}^3={(1+\frac{r}{100})}^3$
Taking cuberoot on both the sides, we get
$\frac{15}{12}=1+\frac{r}{100}$
Thus $r=25$

The rate of interest is $25\%$