Question

On a certain Principal if the Simple interest for two years is $Rs.4800$ and Compound interest for the two years is $Rs.5088$, what is the rate of interest

• A. $6\%$
• B. $24\%$
• C. $12\%$
• D. $18\%$

Answer 1

Answer: (C)

$12\%$

Given, $SI=4800$

$CI=5088$

Say the principal amount was $P$ and rate of interest is $r$% p.a for two years

$\therefore$ $SI=\frac{PT}{100}=\frac{P\times 2\times r}{100}$

$\Rightarrow 4800=\frac{2Pr}{100}$

$\Rightarrow 240000=Pr⟶\left(1\right)$

Similarly $CI=P{(1+\frac{r}{100})}^2-P$

$\Rightarrow 5088=P[{(1+\frac{r}{100})}^2-1]⟶\left(2\right)$

Substituting $\left(1\right)$ in $\left(2\right)$ we get

$5088=\frac{240000}{r}[1+\frac{r^2}{{100}^2}+\frac{2r}{100}-1]$

$\Rightarrow \frac{5088}{240000}=\frac{r}{{100}^2}+\frac{2}{100}$

$\Rightarrow 0.0212=\frac{r}{{100}^2}+0.02$

$\Rightarrow 0.0012=\frac{r}{{100}^2}$

$\therefore$ $r=12$%