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# In how many years will the money deposited in a bank double itself, if the rate of increase is $12\dfrac{1}{2}$ % per annum? Verified
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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 $n$ .

We assume the amount kept in the bank is Rs. $x$ . We need to find the years in the bank in which the money deposited doubles itself, if the rate of increase is $12\dfrac{1}{2}$ % per annum.
We take time in years as $n$ and $r$ as the rate of the bank. Principal amount be $P$ .
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 $A=2x,P=x,r=12\dfrac{1}{2}=\dfrac{25}{2}$ .
Putting the values, we get $2x=x\left( 1+\dfrac{25n}{200} \right)$ . We now simplify the equation.
\begin{align} & 2x=x\left( 1+\dfrac{25n}{200} \right) \\ & \Rightarrow 1+\dfrac{25n}{200}=\dfrac{2x}{x}=2 \\ & \Rightarrow \dfrac{25n}{200}=2-1=1 \\ & \Rightarrow n=\dfrac{200}{25}=8 \\ \end{align}