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A man brought Rs 4000 at 10 percent per annum compounded interest. At the end of each year he has repaid Rs 1000. The amount of money be still incurs after third year is
$\begin{align}
  & \text{a) 2740} \\
 & \text{b) 2104} \\
 & \text{c) 2014} \\
 & \text{d) 3400} \\
\end{align}$

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Last updated date: 17th Jun 2024
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Answer
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Hint: Now we are given that a man borrows 4000 Rs at 10 percent interest compounded annually. Hence we will find the total amount after 1 year with the help of formula of amount for compound interest. The formula for compound interest amount for Principal P, rate r, and time t is given by $A=P{{\left( 1+\dfrac{r}{100} \right)}^{t}}$ . Hence we will get the amount for the first year. Now we know the man pays 1000 yearly hence we will subtract 1000 from the amount. Now the obtained value is the principal amount for next year which is second year. We will continue the process to finally find the amount after 3 years.

Complete step by step answer:
Now a man borrowed 4000 Rs at 10 percent per annum
Now here Principal Amount P = 4000 rate of interest is 10 percent.
Now amount in compound interest is given by $A=P{{\left( 1+\dfrac{r}{100} \right)}^{t}}$ where P is principal amount t is time in years and r is rate of interest in percentage
Hence after 1 year the interest will be.
\[\begin{align}
  & A=4000{{\left( 1+\dfrac{10}{100} \right)}^{1}} \\
 & \Rightarrow A=4000\left( 1+0.1 \right) \\
 & \Rightarrow A=4000\times 1.1 \\
 & \Rightarrow A=4400 \\
\end{align}\]
Hence the final amount is 4400 Rs.
Now let the interest is 4400Rs and he pays 1000 each year hence the remaining interest is 3400.
Now for second year principal is 3400 and rate of interest is 10 percent.
Hence we get the amount after 1 year.
$\begin{align}
  & A=3400{{\left( 1+\dfrac{10}{100} \right)}^{1}} \\
 & \Rightarrow A=3400\left( 1.1 \right) \\
 & \Rightarrow A=3740 \\
\end{align}$
Now again he pays 1000 Rs hence the remaining amount is 3740 – 1000 = 2740 Rs.
Now let us calculate the Compound interest for the third year.
Now principal is 2740, Interest rate is 10 percent
Hence after 1 year the amount will be,
$\begin{align}
  & A=2740{{\left( 1+\dfrac{10}{100} \right)}^{1}} \\
 & \Rightarrow A=2740\left( 1.1 \right) \\
 & \Rightarrow A=3014 \\
\end{align}$
Now again he pays 1000 Rs so the amount remaining is 3014 – 1000 = 2014.
Hence after 3 years the amount remaining is 2014.

So, the correct answer is “Option C”.

Note: Here we cannot directly calculate the interest after 3 years since the principal amount changes after each year. Hence for each year we need to find the total amount and subtract monthly installments to get the final amount.