Vivek borrowed Rs. 20,000 from his friend at 12% per annum simple interest. He lent it to Jyoti at same rate but compounded annually. What would he gain after 2 years?  

Correct option is D

Given:

Principal amount borrowed by Vivek: Rs. 20,000

Rate of interest: 12% per annum

Time period: 2 years

Formula Used:

SI = $$\frac{P \times R \times T}{100}$$​​

CI = $$P \times \left(1 + \frac{R}{100}\right)^T - P$$​​

Solution:

Simple Interest (SI) for Vivek's loan.

​$$= \frac{20000 \times 12 \times 2}{100}$$​​

​$$= \frac{480000}{100}$$​​

= 4800

So, Vivek will pay Rs. 4800 as interest.

Compound Interest (CI) for Jyoti's loan.

CI = $$20000 \times \left(1 + \frac{12}{100}\right)^2 - 20000$$​​

​$$= 20000 \times (1.12)^2 - 20000$$​​

​$$= 20000 \times 1.2544 - 20000$$​​

= 25088 - 20000

= 5088

So, the compound interest earned by Vivek from Jyoti is Rs. 5088

Gain  = 5088 - 4800 = 288

Thus, Vivek will gain Rs. 288 after 2 years.