Question

A man borrows Rs.6000 at 5% compound interest. If he repays Rs.1200 at the end of each year, find the amount outstanding at the beginning of the third year.

Answer 1

Hint: The interest is compounded. So first calculate the final amount after 1 year using the below mentioned formula and subtract 1200 from it to get the amount outstanding at the beginning of the second year. Next this amount will now be the principal amount. Using this principal amount calculate the final amount and subtract 1200 from it to get the amount outstanding at the beginning of the third year or end of the second year.
Formula used:
Final amount A is calculated by $ A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T} $ , where P is the principal amount, T is the time period and R is the compound interest rate.

Complete step-by-step answer:
We are given that a man borrows Rs.6000 at 5% compound interest and he repays Rs.1200 at the end of each year.
We have to calculate the amount outstanding at the beginning of the third year.
Final amount at the end of the first year is $ A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T} $ , here P is Rs.6000, R is 5 and T is 1.
Final amount is
 $ \Rightarrow {A_1} = 6000{\left( {1 + \dfrac{5}{{100}}} \right)^1} = 6000\left( {\dfrac{{105}}{{100}}} \right) = 6000 \times 1.05 = Rs.6300 $
Final amount at the end of 1st year is Rs.6300 and he pays Rs.1200.
So the amount left at the starting of the 2nd year is $ Rs.6300 - Rs.1200 = Rs.5100 $
Now for the second year, Rs. 6300 will be the principal amount.
Final amount at the end of the 2nd year is
 $ \Rightarrow {A_2} = 5100{\left( {1 + \dfrac{5}{{100}}} \right)^1} = 5100\left( {\dfrac{{105}}{{100}}} \right) = 5100 \times 1.05 = Rs.5355 $
And he again pays Rs.1200. So the amount at the end of 2nd year will be $ Rs.5355 - Rs.1200 = Rs.4155 $
The amount at the end of 2nd year is the amount at the beginning of 3rd year that is Rs.4155.
Therefore, the amount outstanding at the beginning of the third year is Rs. 4155.
So, the correct answer is “Rs. 4155”.

Note: The interest can be either simple or compound. In simple interest, the interest amount does not change till the end of the return period whereas in compound interest, the interest amount gradually changes as the interest is imposed on the principal amount plus the previous accumulated interest combined. Compound interest is much greater than Simple interest.