Question

A sum of Rs. 24,000 is lent out for 2 years at compound interest, the rate of interest being 10% per year. The borrower returns some pay at the end of the first year and on paying Rs. 12,540 at the end of the second year the total debt is cleared. Calculate the amount of money returned at the end of the first year.

Answer 1

Hint: To solve this question we must have the knowledge of Interests. Firstly, we will find the interest at the end of \[{{1}^{st}}\] year. Then we will find the interest at the end of \[{{2}^{nd}}\] year. To find the interest, we will use S.I. \[=\dfrac{PRT}{100}\] . To find the amount of money returned at the end of first year, we will subtract the amount of money at the end \[{{2}^{nd}}\] year to the money at the end of \[{{1}^{st}}\] year. We will get our final answer.

Complete step by step answer:
Simple Interest may be defined as the mathematical multiplication of principal P by the interest rate R and by the number of years T and the resultant is divided by 100.
S.I. \[=\dfrac{PRT}{100}\]
Let the amount of money returned at the end of \[{{1}^{st}}\] year be x.
Firstly, we will find the interest of that year,
S.I. for \[{{1}^{st}}\] year \[=\dfrac{PRT}{100}=\dfrac{24000\times 10\times 1}{100}=2400\]
So, the total amount at the end of first year,
\[\begin{align}
  & =\text{Principal}+\text{S}\text{.I}\text{.} \\
 & =24000+2400 \\
 & =26400 \\
\end{align}\]
Similarly, now we will find the interest for \[{{2}^{nd}}\] year
Interest for \[{{2}^{nd}}\] year \[=\dfrac{PRT}{100}=\dfrac{26400\times 10\times 1}{100}=2640\]
So, the total amount at the end of \[{{2}^{nd}}\] year,
\[\begin{align}
  & =\text{Principal}+\text{S}\text{.I}\text{.} \\
 & =26400+2640 \\
 & =29040 \\
\end{align}\]
Now, according to the question, the borrower paid Rs. 12540 in the \[{{2}^{nd}}\] year. The total amount paid by the borrower is Rs. 29040. So, the amount paid by the borrower at the end of \[{{1}^{st}}\] year will be,
\[\begin{align}
  & 29040-x=12540 \\
 & x=29040-12540 \\
 & x=16500 \\
\end{align}\]

Hence, the total amount of money which was returned at the end of \[{{1}^{st}}\] year is Rs. 16,500.

Note: This question is based on Interest, so don’t get confused in Simple Interest and Compound Interest, as both of them are different. Also, the total amount of money at the end of \[{{2}^{nd}}\] year means the money of both the years, not only of the second year (includes the amount of money at the end of the first year).
We can find the amount using the direct formula of CI as well.