Question

Ranbir borrows Rs. 20,000 at 12% per annum compound interest. If he repays Rs. 8400 at the end of the first year and Rs.9680 at the end of the second year, find the amount of loan (in Rs.) outstanding at the beginning of the third year.

Answer 1

- Hint: We will first calculate the compound interest for the first year. Then, we will calculate the compound interest for the second year and then, the amount that will be left with us would be the outstanding at the beginning of the third year.

Complete step-by-step solution -

Given that Ranbir borrowed Rs.20000 at 12% compound interest.
For First year:-
Interest \[=\dfrac{20000\times 1\times 12}{100}=Rs.2400\] .
Thus, amount after one year = Rs.20000 + Rs.2400 = Rs.22400
Money repaid by Ranbir = Rs.8400
∴ Balance = Rs.22400 − Rs.8400 = Rs.14000
For Second year:-
Interest \[=\dfrac{14000\times 1\times 12}{100}=Rs.1680\] .
Thus, amount after second year = Rs.14000 + Rs.1680 = Rs.15680
Money repaid by Ranbir = Rs.9680
∴ Balance = Rs.15680 – Rs.9680 = Rs. 6000
Hence, loan outstanding at the beginning of the third year = Rs.6000
Therefore, the answer of this question is Rs.6000.

Note:- Let us now know why we have calculated the answer of this question using the formula of simple interest and not compound interest.
Here in this question, we have broken the compound interest yearly and we are taking one year into consideration at a time, so, compound interest is something in which the principal amount changes as the time progresses and as we are taking one year at a time, therefore, compound interest will be equal to simple interest for this consideration.