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Last updated date: 01st Dec 2023
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MVSAT Dec 2023

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?

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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 $ .

Complete step-by-step answer:
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} $
The number of years is 8.
So, the correct answer is “8 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.