Question

A man borrows Rs. 6000 at 5% Compound Interest per annum. If the man repays Rs.1200 at the end of each year, find the amount of the loan outstanding at the beginning of the third year.
(a) Rs.4155.00
(b) Rs.5555.50
(c) Rs.5452.00
(d) Rs.4452.50
(e) None of these

Answer 1

Hint: We have the formula of Compound Interest as \[CI=\dfrac{PR}{100}\], where P is the Principal, R is the rate of interest. We will use this formula to solve the given question.

Complete step-by-step answer:
Given that the man borrowed Rs.6000 therefore, the Principal \[P=6000\]
The rate of interest is 5% per annum therefore, we have \[R=5%\]
Now we put the above values in the formula of Compound interest as \[CI=\dfrac{PR}{100}\] separately for each year and solve it accordingly.
i.e. CI for the first year will be
\[C{{I}_{1}}=\dfrac{\left( 6000 \right)\left( 5 \right)}{100}\]
\[\begin{align}
  & \Rightarrow C{{I}_{1}}=\dfrac{30000}{100} \\
 & \\
 & \Rightarrow C{{I}_{1}}=300 \\
\end{align}\]
The CI for the first year is Rs. 300.
Now, the formula for total amount after including the CI of first year is
\[A=P+C{{I}_{1}}\]
 Substituting the corresponding values, we get
\[A\]= 6000+300
 \[\Rightarrow \]\[A\]= Rs 6300
Since he pays Rs 1200 at the end of every year so the amount outstanding at the beginning of the second year will be
= 6300-1200 = Rs.5100, and this becomes the principal of the second year.
Hence, we get the principle for the second year as
\[{{P}_{2}}=5100\]
Again, the CI for the second year will be
\[C{{I}_{2}}=\dfrac{PR}{100}\]
Now we putting the values in the above formula we get,
\[C{{I}_{2}}=\dfrac{\left( 5100 \right)\left( 5 \right)}{100}=255\]
Now after solving this we get
\[C{{I}_{2}}=255\]
Now the amount for the second year after adding \[C{{I}_{2}}\]and the \[{{P}_{2}}\] we get \[{{A}_{2}}\]
\[{{A}_{2}}={{P}_{2}}+C{{I}_{2}}\]

\[\begin{align}
  & \Rightarrow {{A}_{2}}=5100+255 \\
 & \\
 & \Rightarrow {{A}_{2}}=5355 \\
\end{align}\]

Since, he has to pay Rs.1200 at the end of every year.
So, the amount at the beginning of the 3rd year will be 5355-1200.
 the amount at the beginning of the 3rd year will be Rs.4155.
Hence, we get the amount of the loan outstanding at the beginning of the third year is Rs 4155.00 i.e. option (a).

Note: The possibility of error can be, not subtracting Rs.1200 to the amount at the end of each year because the man repays Rs.1200 at the end of each year. Also be careful while calculating the interest as a small error can make a big mistake and remember that the interest is to be calculated on Principal and not amount.