Question

Rs. $100000$ was invested by Mohan in a fixed deposit at $10\%$ per annum at CI. However every year he was to pay $20\%$ tax on the compound interest. How much money does Mohan has after $3$ years?
(a) Rs. $128414$
(b) Rs. $108000$
(c) Rs. $126079.2$
(d) Rs. $12971.2$

Answer 1

Hint: We need to use the formula for the compound interest, which is given by $I=\dfrac{P\times R}{100}$ to calculate the compound interest earned each year. Then, we need to deduct the tax of $20\%$ on the compound interest for each year. Then after adding the compound interest and subtracting the tax from the amount for each year. Following this three times, we will get the amount possessed by Mohan after three years.

Complete step by step solution:
According to the above question, the initial investment made by Mohan, or the principle amount is
$\Rightarrow P=100000......\left( i \right)$
And the rate is given as
$\Rightarrow R=10......\left( ii \right)$
We know that the compound interest earned annually is given by
$\Rightarrow I=\dfrac{P\times R}{100}$
Substituting (i) and (ii) we get
$\begin{align}
  & \Rightarrow I=\dfrac{100000\times 10}{100} \\
 & \Rightarrow I=10000 \\
\end{align}$
According to the question, he pays $20\%$ tax on the compound interest. Therefore, the tax paid by him in the first year is
$\begin{align}
  & \Rightarrow T=10000\times \dfrac{20}{100} \\
 & \Rightarrow T=2000 \\
\end{align}$
So the amount after the first year becomes
$\begin{align}
  & \Rightarrow A\left( 1 \right)=P+I-T \\
 & \Rightarrow A\left( 1 \right)=100000+10000-2000 \\
 & \Rightarrow A\left( 1 \right)=108000 \\
\end{align}$
Similarly, the compound interest earned by Mohan in the second year is
$\begin{align}
  & \Rightarrow I=\dfrac{108000\times 10}{100} \\
 & \Rightarrow I=10800 \\
\end{align}$
And the tax paid in the second year is
$\begin{align}
  & \Rightarrow T=10800\times \dfrac{20}{100} \\
 & \Rightarrow T=2160 \\
\end{align}$
Therefore, the amount after the second year is
$\begin{align}
  & \Rightarrow A\left( 2 \right)=108000+10800-2160 \\
 & \Rightarrow A\left( 2 \right)=116640 \\
\end{align}$
Similarly, the compound interest earned by Mohan in the second year is
$\begin{align}
  & \Rightarrow I=\dfrac{116640\times 10}{100} \\
 & \Rightarrow I=11664 \\
\end{align}$
And the tax paid in the second year is
$\begin{align}
  & \Rightarrow T=11664\times \dfrac{20}{100} \\
 & \Rightarrow T=2332.8 \\
\end{align}$
Therefore, the amount after the second year is
$\begin{align}
  & \Rightarrow A\left( 3 \right)=116640+11664-2332.8 \\
 & \Rightarrow A\left( 3 \right)=12971.2 \\
\end{align}$
Thus, the amount that Mohan has after three years is equal to Rs. $12971.2$.

So, the correct answer is “Option d”.

Note: Since it is given in the question that the tax at the rate of $20\%$ per year on the compound interest, do not compound the initial investment for the three years at once only. We need to deduct the tax for each year and hence we need to calculate the amount for each of the years, as shown in the above solution.