Question

Mr sharma borrowed rs 20000 from his friend Mr base at the rate of 18% per annum simple interest for 2 years.He lent this money to Mr Gupta at the same rate but compounded annually find his gain after 2 years

Answer 1

Mr Sharma borrowed Rs. 20000 
rate = 18% (simple)
time = 2 years

$I = \frac{Ptr}{100} = \frac{20000*2*18}{100} =Rs.7200$

Total amount he will return to Mr Sharma = 20000+7200 = Rs. 27200

Mr. Sharma lent Rs. 20000 
rate = 18% (compound)
time = 2 years
Let the total amount he will get at the end of years = A

$A=P(1+r) ^{t} = 20000(1+0.18) ^{2}=20000*1.18 ^{2} \\ \\ A=20000*1.3924=Rs.27848$

Gain = amount he will get - amount he will give 
        = Rs. 27848 - Rs. 27200
        = Rs. 648

Answer 2

The difference between simple interest and compound interest is the interest calculated on the interest accumulated till last year.

Simple Interest for 1 years = 20, 000 * 18/100 * 1 = Rs 3,600

The additional amount gained by compounding interest is
        = Rs 3,600 * 18/100 * 1 year  = Rs 648