Amit borrowed a sum of ₹25,000 on simple interest. Bhola borrowed the same amount on compound interest(interest compounded yearly). At the end of 2 years, Bhola had to pay ₹160 more interest than Amit. The rate of interest charged per annum is:

Difference of the compound interest and simple interest = 160

$$p(1 + \frac{r}{100})^t - p - \frac{prt}{100} = 160$$

p = 25000

t = 2

 $$25000(1 + \frac{r}{100})^2 - 25000 - \frac{25000 \times r \times 2}{100} = 160$$

$$25000(1 + (\frac{r}{100})^2 + \frac{2r}{100}) - 25000 - \frac{25000 \times r \times 2}{100} = 160$$

$$25000 \times (\frac{r}{100})^2 = 160$$

$$r^2 = 160/2.5$$

$$r^2 = 64$$

r = 8%

$$\therefore$$ The rate of interest is 8%.