Question

A sum of money becomes Rs. $13380$ after $3$ years and Rs. $20070$ after $6$ years on compound interest. The sum is

• A. Rs. $8800$
• B. Rs. $8890$
• C. Rs. $8920$
• D. Rs. $9040$

Answer 1

The correct option is C Rs. $8920$

Let the sum be $Rs.x$

Then

$P{(1+\frac{R}{100})}^n=A$ ....(a)

where $P=$ Sum, $R=$ rate of interest and $N=$ time (in years)
$x{(1+\frac{R}{100})}^3=13380$ ....... (i)
and $x{(1+\frac{R}{100})}^6=20070$ ........ (ii)
Dividing equation (ii) by (i), we get
${(1+\frac{R}{100})}^3=\left(\frac{20070}{13380}\right)$

$=\left(\frac{3}{2}\right)$

Put in (a),
$\therefore x\times \frac{3}{2}=13380$
$\Rightarrow x=(13380\times \frac{2}{3})$

$=Rs.8920$

Required result is $=Rs.8920$