Question

A sum of money, invested at compound interest, amounts to Rs. $19,360$ in $2$ years and to Rs. $23,425.60$ in $4$ years. Find the rate per cent and the original sum of money.

• A. $10$% and Rs. $17,000$
• B. $19$% and Rs. $25,637$
  
• C. $10$% and Rs. $16,000$
• D. $19$% and Rs. $26,634$
  

Answer 1

The correct option is C $10$% and Rs. $16,000$

Amount for $4$ years $=Rs.23425.50$
Amount for $2$ years $=Rs.19360$
Let the rate of interest $=R$ $\%$
$A=P{(1+\frac{R}{100})}^T$
$23425.50=19360{(1+\frac{R}{100})}^2$

$\Rightarrow {(1+\frac{R}{100})}^2=\frac{23425.50}{19360}$

$\Rightarrow {(1+\frac{R}{100})}^2=\frac{121}{100}$

$\Rightarrow 1+\frac{R}{100}=\frac{11}{10}$

$\Rightarrow \frac{R}{100}=\frac{1}{10}$

$\Rightarrow R=10$
Now Amount $=$ Rs. $19360$, $R=10$ $\%$, Time $=2$ years
$19360=P{(1+\frac{10}{100})}^2$
$\Rightarrow 19360=P{\left(\frac{11}{10}\right)}^2$
$\Rightarrow P=\frac{19360\times 10\times 10}{11\times 11}$
$\Rightarrow P=Rs.16000$