Question

At what rate per cent per annum will a sum of Rs. $7500$ amount to Rs. $8427$ in $1\frac{2}{2}$ years, compounded annually?

• A. $8\%$
• B. $6\%$
• C. $5\%$
• D. $4\%$

Answer 1

The correct option is B $6\%$

We know the formula,
$A=P{(1+\frac{r}{n})}^{n.t}$
Where,
$A=$ total amount
$P=$ principal or amount of money deposited,
$r=$ annual interest rate
$n=$ number of times compounded per year
$t=$ time in years
Given, $A=$ Rs. $8427$, $P=$ Rs. $7500$, $n=1$ and $t=$ $1\frac{2}{2}$ years
$\Rightarrow 8427=7500{(1+\frac{r}{1})}^{1\times 2}$
$\Rightarrow \frac{8427}{7500}={(1+\frac{r}{1})}^2$
$\Rightarrow {(1+\frac{r}{1})}^2=1.1236$
Take the natural logarithm of each side
$2.\ln (1+\frac{r}{1})=\ln \left(1.1236\right)$
$\Rightarrow 1+\frac{r}{1}=e^{0.05827}$
$\Rightarrow 1+\frac{r}{1}=1.06000$
$\Rightarrow r=0.0600$ $\approx 6$ $\%$