A sum of ₹18,000 is lent at 10% p.a. compound interest. compounded annually. What is the difference between the compound interest for $$3^{rd}$$ year and $$4^{th}$$ year?

Compound interest = $$p(1 + \frac{r}{100})^t - p$$
Amount at the end of 2 years = $$18000 (1+10/100)^2$$

= $$18000 (1.1)^2$$ = Rs 21780

Amount at the end of 3 years = 18000 (1+10/100)3(1+10/100)3= Rs 23958

Interest for 3rd year = Amount at end of 3rd year - Amount at end of 2nd year = 23958 - 21780 = Rs 2178

Amount at the end of 4 years = $$18000(1+10/100)^4 $$= Rs 26353.8

Interest for 4th year = Amount at end of 4th year - Amount at end of 3rd year = 26353.8 - 23958 = Rs 2395.8

Difference between interest of 3rd year and of 4th year = 2395.8 - 2178 = Rs 217.8