Question

Rajesh deposits a certain amount in the bank which becomes three times of itself in 16 years. Find the time required by the same amount to become four times of itself.

Answer 1

Hint: We first use the general formula of simple interest where we have $A=P\left( 1+\dfrac{rn}{100} \right)$ for time in years as $n$, $r$ as rate of the bank and principal amount as $P$. We get the equation and solve to find the value of $n$.

Complete step by step answer:
We assume the amount kept in the bank is Rs. $x$. We have that the deposited amount gets three times of itself in 16 years. We take time in years as $n$ and $r$ as the rate of the bank. Principal amount is $P$. Now if $A$ is the final amount consisting of both principal and interest then $A=P\left( 1+\dfrac{rn}{100} \right)$. It is given that $A=2x,P=x,n=16$.Putting the values, we get $2x=x\left( 1+\dfrac{16r}{100} \right)$. We now simplify the equation.
$\Rightarrow 2x=x\left( 1+\dfrac{16r}{100} \right) \\
\Rightarrow 1+\dfrac{16r}{100}=\dfrac{2x}{x}=2 \\
\Rightarrow \dfrac{16r}{100}=2-1=1 \\
\Rightarrow r=\dfrac{100}{16}=\dfrac{25}{4} \\ $
We have to find the number of years the deposited amount becomes four times.
Therefore, $4x=x\left( 1+\dfrac{25n}{400} \right)$. Simplifying we get
$4x=x\left( 1+\dfrac{25n}{400} \right) \\
\Rightarrow 1+\dfrac{25n}{400}=4 \\
\Rightarrow \dfrac{n}{16}=4-1=3 \\
\therefore n=3\times 16=48 $

Therefore, the time required is 48 years.

Note: Simple interest paid or received over a certain period is a fixed percentage of the principal amount that was borrowed or lent. Compound interest accrues and is added to the accumulated interest of previous periods, so borrowers must pay interest on interest as well as principal.