Question

A sum amounts to Rs. 2,916 in 2 years and Rs. 3,194.28 in 3 years when compounded annually. Find the principal.

Answer 1

Amount at the end of the second year $=2,916$ Rs. .... [Given]

Amount at the end of the third year $=3,194.28$ Rs. ...... [Given]

Amount at the end of the second year = Principal for the second year

$\therefore P=2,916$

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

$\Rightarrow 3194.28=2916{(1+\frac{R}{100})}^1$

$\Rightarrow \frac{3194.28}{2916}=1+\frac{R}{100}$

$\Rightarrow 1.0954=1+\frac{R}{100}$

$\Rightarrow R=9.5\%$

Amount at the end of $2$nd year is $2916$

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

$\Rightarrow 2916=P{(1+\frac{9.5}{100})}^2$

$\Rightarrow 2916=P{\left(\frac{109.5}{100}\right)}^2$

$\Rightarrow \frac{2916\times 100\times 100}{109.5\times 109.5}=P$

$\Rightarrow P=2431.975$ thus we can say $P\sim 2432$ Rs.

Thus, $P=Rs.2432$

Hence, the principal is Rs. $2,432$.