Question

In how many years will Rs. $6750$ amount to Rs. $8192$ at $6\frac{2}{3}\%p.a$ compounded annually?

Answer 1

Given :

$P=6750,A=8192,r=6\frac{2}{3}=\frac{20}{3}$

Formula : $A=P{(1+\frac{r}{100})}^n$

$\therefore 8192=6750{(1+\frac{20}{3\times 100})}^n$

$\Rightarrow \frac{8192}{6750}={\left(\frac{16}{15}\right)}^n$

$\Rightarrow \frac{16\times 16\times 16\times 2}{15\times 15\times 15\times 2}={\left(\frac{16}{15}\right)}^n$

$\Rightarrow n=3$

In $3$ years Rs. $6750$ amount to Rs. $8192$ at $6\frac{2}{3}$% rate compounded annually.