Question

A sum of money is lent out at compound interest at a certain rate per annum becomes three times of itself in $8$ years.Find in how many years will the money become $27$ times of itself at the same rate of interest per annum.

Answer 1

Let the sum of money be Rs $P$ and the rate of interest be $r\%$ p.a.

Amount at the end of $8$ years $=$ Rs $3P$

Formula for amount$=P{(1+\left(\frac{r}{100}\right))}^n$

where $n=$time,$p=$principal and $r=$rate

$\Rightarrow 3P=P{(1+\frac{r}{100})}^8$

$\Rightarrow 3={(1+\frac{r}{100})}^8$ .........$\left(1\right)$

Let the money becomes $27$ times in $n$ years

$\Rightarrow 27={(1+\frac{r}{100})}^n$

$\Rightarrow {\left({(1+\frac{r}{100})}^8\right)}^3={(1+\frac{r}{100})}^n$

comparing both the bases, we get

$n=8\times 3=24$