Question

In what time will $Rs.2000$ amount to $Rs.2205$ at $5\%$ per annum, compounded annually?

Answer 1

$P=Rs.2000$

$R=5\%$

$A=Rs.2205$

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

$\Rightarrow 2205=2000{(1+\frac{5}{100})}^n$

$\Rightarrow \frac{2205}{2000}={\left(\frac{105}{100}\right)}^n$

$\Rightarrow \frac{441}{400}={\left(\frac{21}{20}\right)}^n$

$\Rightarrow {\left(\frac{21}{20}\right)}^2={\left(\frac{21}{20}\right)}^n$

$\because$ Powers are equal if bases are equal $n=2$ i.e., Time $=2$ years