Question

A man borrowed Rs.5000 at 20% per annum compound interest. At the end of each year he has repaid Rs.3000 the amount of money he still incurs after the third year is?
(a) Rs.2740
(b) Rs.2104
(c) Rs.3180
(d) Rs.3400

Answer 1

Hint: To solve this problem we need to first know that how to find the X% of a quantity Y. X% of the Y would be given as $X\%\,of\,Y\,=\dfrac{X}{100}\times Y$. So first of all we will find the 20% of 5000 and then add that amount with 5000 and then we will subtract 3000 from the obtained amount and get the amount that the man will incur at the end of first year. After that we will proceed similarly for 2 more times to find the final answer i.e. amount the man incur at the end of three years.

Complete step-by-step solution:
We are given that a man borrowed Rs.5000 at 20% per annum and he repays Rs3000 at the end of the each year,
We have to find the amount that he incurs at the end of third year i.e. the amount that he still has to pay after three years.
But first we have to know that how can we calculate percentage,
Y% of the Z amount is given by = $\dfrac{Y}{100}\times Z$
Now we will solve this problem in three steps that is one for each year,
First we have principle amount as Rs.5000 and interest 20%,
So at the end of the first year he has to pay = 5000 + $\dfrac{20}{100}\times 5000$
$\begin{align}
  & =5000+1000 \\
 & =6000 \\
\end{align}$
Now the man repays Rs1500 so he has left with,
= 6000 – 1500
= 4500
Now we will solve for second year,
At the end of the second year he has to pay = 4500 + $\dfrac{20}{100}\times 4500$
= 4500 + 900
= 5400
The man repays Rs 1500 so he has left with,
= 5400 – 1500
= 3900
Now we will solve for third year as,
At the end of the second year he has to pay = 3900 + $\dfrac{20}{100}\times 3900$
= 3900+780
= 4680
The man repays Rs1500 so he has left with,
= 4680-1500
= 3180
Hence at the end of third year man is left with Rs.3180 so we get option (c) as the correct answer.

Note: Some students here might just calculate the compound interest here for 3 years using its formula and then subtract 1500 from the total obtained amount but that would be wrong as in that case we will get the interest on whole amount 5000 for 3 years and not on the reduced amount for each year so be careful about that.