Question

A sum of money invested at a certain rate of interest doubles itself in $10$ years. In how many years will the money triple itself at the same rate?

Answer 1

Let the amount of money invested be $Rs.x$ and the rate of interest be $r\%$ per annum.

Given that the money doubles in $10$ years.

Therefore, amount after $10$ years $=Rs.2x$

$\text{Amount}=\text{Principal amount}+\text{Interest}$

Also, $\text{Interest}=\frac{P\times R\times T}{100}$

$\therefore 2x=x+\frac{x\times r\times 10}{100}$

$\Rightarrow x=\frac{x\times r\times 10}{100}$

$\Rightarrow r=10$

Hence, rate of interest $=10\%$

Now, let $t$ be the years required for the amount to triple at the same rate of interest.

Triple amount $=Rs.3x$

$\therefore 3x=x+\frac{x\times 10\times t}{100}$ $[R=10\%\text{and}P=x]$

$\Rightarrow 2x=\frac{x\times 10\times t}{100}$

$\Rightarrow t=20$

Hence, the money will triple itself at the same rate of interest in $20$ years.