Question

In how many years will Rs 800 amount to Rs 882 at 5% per annum compounded annually?

Answer 1

Here, P = Rs 800
A = Rs 882
r = 5% p.a.
Let number of years be n.
Since, A = P ${(1+\frac{r}{100})}^n$

$\therefore 882=800{(1+\frac{5}{100})}^n=800{(1+\frac{1}{20})}^n$

$or\frac{882}{800}={(1+\frac{1}{20})}^n$

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

$or{\left(\frac{21}{20}\right)}^2={\left(\frac{21}{20}\right)}^n[\because 441={21}^{2}and400={20}^2]$
Since the bases are same on both sides, hence n = 2
Since interest is compounded annually.
$\therefore$ Time = 2 years.