On a certain sum of money, the simple interest for 2 years is ₹150 at the rate of 10% per annum. What is the difference between compound interest and simple interest for 2 years if, in the case of compound interest, interest is compounded annually at the rate of 10% per annum?

On a certain sum of money, the simple interest for 2 years is ₹150 at the rate of 10% per annum.

simple interest = $$\frac{principal\times rate\times\ time\ }{100}$$

$$150=\frac{principal\times10\times2\ }{100}$$

principal = $$150\times5$$ = ₹750

compound interest = $$principal\left[\left(1+\frac{rate}{100}\right)^2-1\right]$$

= $$750\left[\left(1+\frac{10}{100}\right)^2-1\right]$$

= $$750\left[\left(1+\frac{1}{10}\right)^2-1\right]$$

Difference between compound interest and simple interest for 2 years = ₹157.5 - ₹150

= ₹7.5