Question

what sum will amount to Rs.32,448 in 2 years at the rate of 4% p.a compounded annually​

Answer 1

Given :

Amount : ₹32448

Rate of interest : 4%

Time : 2 years

To find :

The sum or the principle amount.

Solution :

To find the principle, we use the formula of amount compounded annually.

Principle :

$\sf \dashrightarrow Amount = Principle \bigg( 1 + \dfrac{Rate}{100} \bigg)^{Time}$

$\sf \dashrightarrow 32448 = P \bigg( 1 + \dfrac{4}{100} \bigg)^{2}$

$\sf \dashrightarrow 32448 = P \bigg( 1 + \dfrac{1}{25} \bigg)^{2}$

$\sf \dashrightarrow 32448 = P \bigg( \dfrac{25 + 1}{25} \bigg)^{2}$

$\sf \dashrightarrow 32448 = P \bigg( \dfrac{26}{25} \bigg)^{2}$

$\sf \dashrightarrow 32448 = P \bigg( \dfrac{26^2}{25^2} \bigg)$

$\sf \dashrightarrow 32448 = P \bigg( \dfrac{676}{625} \bigg)$

$\sf \dashrightarrow 32448 = \dfrac{676P}{625}$

$\sf \dashrightarrow 676P = 625(32448)$

$\sf \dashrightarrow 676P = 20280000$

$\sf \dashrightarrow P = \dfrac{20280000}{676}$

$\sf \dashrightarrow P = 30000$

Hence, the principle amount(sum) is ₹30000.