Question

What amount of money should mohan in a bank in order to get $Rs.1323$ in $2$ years at $5\%$ compounded annually ?

Answer 1

Given:

Compound interest in two years $(A-P)=Rs.1323$

Time $\left(n\right)=2$ years

Rate of interest $\left(R\right)=5\%$ per annum

Principal $\left(P\right)=?$

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

Now,

$A-P=Rs.1323$

$\Rightarrow P{(1+\frac{R}{100})}^n-P=1323$

$\Rightarrow P{(1+\frac{5}{100})}^2-P=1323$

$\Rightarrow P({(1+\frac{5}{100})}^2-1)=1323$

$\Rightarrow P({\left(\frac{105}{100}\right)}^2-1)=1323$

$\Rightarrow P\left(\frac{(105{)}^2-(100{)}^2}{(100{)}^2}\right)=1323$

$\Rightarrow P\left(\frac{(105+100)(105-100)}{(100{)}^2}\right)=1323$

$\Rightarrow P\left(\frac{\left(205\right)\left(5\right)}{10000}\right)=1323$

$\Rightarrow P\left(\frac{1025}{10000}\right)=1323$

$\Rightarrow P=1323\times \frac{10000}{1025}$

$\Rightarrow P=\frac{13230000}{1025}$

$\Rightarrow P=12907.3$ (Approximately)

Therefore, the required amount is $Rs.12907.30$ (Approximately)