A sum of money amounts to Rs.6000 in 4 years and to Rs.6750 in 5 years (interest is compounded annually). What is the rate of interest?

Let the principal be Rs.P
We know that amount for Compound Interest = $$P(1+\dfrac{R}{100})^T$$ where P = Principal, R = Rate of interest, T = Time period
Given, $$P(1+\dfrac{R}{100})^4 = 6000$$ and $$P(1+\dfrac{R}{100})^5 = 6750$$

Dividing above equations
$$\dfrac{P(1+\dfrac{R}{100})^5}{P(1+\dfrac{R}{100})^4} = \dfrac{6750}{6000}$$

=> $$1+\dfrac{R}{100} = \dfrac{9}{8}$$

=> $$\dfrac{R}{100} = \dfrac{9}{8} - 1$$

=> $$\dfrac{R}{100} = \dfrac{1}{8}$$

=> R = 12.5%
Therefore, Rate of interest = 12.5%