Question

A sum of money becomes $3$ times in $12$ years . In how many years will it become $5$ times at the same rate of simple interest?

Answer 1

Let, Principal amount be $P$.

Rate of interest be $R$ per annum.

Time of investment is $\left(T\right)=12$ years.

Sum of the money becomes three times in $12$ years.

$\Rightarrow A=3P$.

$\Rightarrow A=P+\left(\frac{P\times T\times R}{100}\right)$

$\Rightarrow 3P=P(1+\frac{T\times R}{100})$

$\Rightarrow 3=1+\frac{12\times R}{100}$

$\Rightarrow 3-1=\frac{12R}{100}$

$\Rightarrow 2=\frac{3R}{25}$

$\Rightarrow 50=3R$

$\Rightarrow \frac{50}{3}=R$

Now, we need to find the number of years $T$ such that, Sum of the money becomes five times.

$\Rightarrow 5P=P(1+\frac{T\times R}{100})$

$\Rightarrow 5=1+\frac{T\times 50}{3\times 100}$

$\Rightarrow 5-1=\frac{T\times 1}{3\times 2}$

$\Rightarrow 4=\frac{T}{6}$

$\Rightarrow 24=T$

will it become $5$ times at the same rate of simple interest $24$ years.