Question

In what period of time will Rs. 12,000 yield Rs. 3,972 as compound interest at 10 per cent, if compounded on an yearly basis.

Answer 1

Given : P = Rs. 12000 ; C.I. = Rs. 3972 and r = 10%
$\Rightarrow$ Amount A = P + I
= Rs. 12000 + Rs. 3972 = Rs. 15972
$\therefore 15972=12000{(1+\frac{10}{100})}^n\because A=P{(1+\frac{r}{100})}^n$
$\Rightarrow \frac{15972}{12000}={\left(\frac{11}{10}\right)}^n$
$\Rightarrow {\left(\frac{11}{10}\right)}^3={\left(\frac{11}{10}\right)}^n[\because \frac{15972}{12000}=\frac{2\times 2\times 3\times 11\times 11\times 11}{2\times 2\times 3\times 10\times 10\times 10}]$
$\Rightarrow n=3$
$\therefore$ Required time = 3 years.