Question

A man borrows Rs. 5,800 at 12% per annum compound interest. He repays Rs. 1,800 at the end of every six months. Calculate the amount standing at the end of the third payment. Give your answer to the nearest rupee.

Answer 1

Hint:
As we need to calculate the standing amount after the third payment, we have to solve this question in three steps. After every instalment paid the principal amount will be changed. The new principal amount will be the previous principal added with interest added in that period minus the instalment paid.

Complete step by step solution:
So, we will take the values for the first six months:
Principal = Rs. 5,800
Time period = \[\dfrac{1}{2}\]​year
Rate of interest = 12 %
We have Simple Interest\[ = \dfrac{{PNR}}{{100}} = \dfrac{{5,800 \times \dfrac{1}{2} \times 12}}{{100}} = Rs348\]
And Amount at the end of first 6 months is
Principal +Simple Interest \[ = Rs5,800 + Rs348 = Rs6,148\]
Now, for the second half year
Principal =\[Rs6,148 - Rs1,800 = Rs4,348\;\]
Time Period =\[\dfrac{1}{2}\]​year
Rate of Interest = 12 %
We have Simple Interest \[ = \dfrac{{PNR}}{{100}} = \dfrac{{4,348 \times \dfrac{1}{2} \times 12}}{{100}} = Rs260.88\]
And amount need to be paid at the end of second half - year
Principal +Simple Interest \[ = Rs4,348 + Rs260.88 = Rs4,608.88\]
Also, for the third half year
Principal =\[Rs4,608.88 - Rs1,800 = Rs2,808.88\;\]
 Time Period =\[\dfrac{1}{2}\]​year
Rate of Interest = 12 %
We have Simple Interest \[ = \dfrac{{PNR}}{{100}} = \dfrac{{2,808.88 \times \dfrac{1}{2} \times 12}}{{100}} = Rs168.5328\]
And amount needed to be paid at the end of third half - year
Principal +Simple Interest \[ = Rs2,808.88 + Rs168.5328 = Rs2,977.4128\]
And after the third payment amount outstanding =\[Rs2,977.4128 - Rs1,800 = Rs1177.4128\;\]

So, the amount standing at the end of the third payment is approximately Rs 1177 to nearest rupee.

Note:
The interest calculated for the first month or period remains equal in both Simple Interest and Compound Interest. From the second month, the interest starts changing. Suppose, if we make a deposit that pays compounded interest, then we will receive interest payments on the original amount that we deposited, as well as additional interest payments. So, the amount at the end of first year (or Period) will become the principal for the second year (or Period) and the amount at the end of second year (or Period) becomes the Principal of third year. So, if you change the principal after every time period of rate of interest by adding the interest into the original principal you can use simple interest formulas in compound interest problems as we have done in this question.