Question

Hari borrowed Rs.28000 from her friend at 12% per annum simple interest. She lends it to Ali at the same rate but compounded annually, find her gain after two years.

Answer 1

Hint: Using the formula of simple interest, calculate the amount that has to be paid by Hari to her friend, then using the formula of compound interest calculate the amount that has to be paid by Ali to Hari. The difference between these two amounts will tell you the amount of money made by Hari in 2 years.

Complete step-by-step answer:
Money is never borrowed for free, the lender applies interest on it to receive more money than he lent.
Interests are of two types:
Simple interest can be calculated by the formula,
 $ \Rightarrow I = \dfrac{{\Pr t}}{{100}} $ , where $ I = $ simple interest, $ r = $ interest, $ P = $ amount borrowed (also called ‘Principal’) and $ t = $ time for which amount is borrowed.
Amount to be repaid is,
 $ \Rightarrow A = P + \dfrac{{\Pr t}}{{100}} = P(1 + \dfrac{{rt}}{{100}}) $
Now, Hari has borrowed Rs.28000 from her friend at an interest of 12% per annum and has to repay the amount after 2 years, so we have - $ P = 28000 $ , $ r = 12 $ and $ t = 2 $ .
Therefore the amount paid by Hari to her friend is,
$ {A_H} = 28000(1 + \dfrac{{12}}{{100}} \times 2) = 28000 \times 1.24 = 31000 $
Amount to be repaid on compound interest can be calculated by the formula,
 $ \Rightarrow A = P{(1 + \dfrac{r}{{100}})^n} $ , where $ A = $ final amount, $ P = $ the amount borrowed, $ r = $ interest and $ n = $ number of periods.
Here, Hari lent Rs.28000 to Ali on interest of 12% for two years, so we have - $ P = 28000 $ , $ r = 12 $ and $ n = 2 $ .
Amount to be repaid is,
 $ \Rightarrow A = 28000{(1 + \dfrac{{12}}{{100}})^2} = 28000{(1.12)^2} = 35123.2 $
Hari will receive Rs.35123.2 from Ali and give Rs.31000 to her friend, so her gain after two years is $ = 35123.2 - 31000 = 4123.2 $
Hence, he made a gain of Rs.4123.2.
So, the correct answer is “Rs.4123.2”.

Note: The interest that is calculated only on the amount taken and is the same for the annual period is called simple interest.
Compound interest:
In the case of compound interest, we calculate the interest for the first period and then add it to the amount borrowed, then calculate the interest for the next period using the new amount and so on.
Keeping these two definitions in mind solve the question carefully.