Question

A sum of money becomes $\text{Rs.}6,500$ after $3$ years and $\text{Rs.}10,562.50$ after $6$ years on compound interest. Find the initial amount of the money.

• A. $\text{Rs.}4,000$
• B. $\text{Rs.}4,500$
• C. $\text{Rs.}4,800$
• D. None of these

Answer 1

Answer: (A)

$\text{Rs.}4,000$

Let the initial amount of money be $P$.

$A=P{(1+\frac{R}{100})}^T$ where $R=$ Rate of Interest and $T=$ Time period.

Amount after $3$ years $=6500$

$\Rightarrow 6500=P{(1+\frac{R}{100})}^3⟶\left(I\right)$

Amount after $6$ years $=10,562.5$

$\Rightarrow 10562.5=P{(1+\frac{R}{100})}^6⟶\left(II\right)$

From eq$\left(I\right)$,

$\frac{6500}{P}={(1+\frac{R}{100})}^3$

$\Rightarrow {\left(\frac{6500}{P}\right)}^2={(1+\frac{R}{100})}^6⟶\left(III\right)$

Putting eq$\left(III\right)$ in eq$\left(II\right)$

$10562.5=P{\left(\frac{6500}{P}\right)}^2$

$\Rightarrow 10562.5=P\times \frac{{\left(6500\right)}^2}{P^2}$

$\Rightarrow P=\frac{{\left(6500\right)}^2}{10562.5}$

$=4000$

Hence, the initial amount of money is equal to $\text{Rs.}4000$.