A sum of ₹15,000 is lent at 16% p.a. compound interest. What is the difference between the compound interest for the second year and the third year?

As per given question

$$A=P( 1+\dfrac{R}{100})^2$$

$$A_1=15000(1+\dfrac{16}{100})^2$$

Compound interest in the first year $$=15000(1+\dfrac{16}{100})=116\times150=17400$$

So, compound interest in 2nd year$$=A_1-P=15000(1+\dfrac{16}{100})^2-17400=20184-17400=2784$$---------(i)

Similarly

$$A_2=15000(1+\dfrac{16}{100})^3$$

So, compound interest in 3rd year $$=A_2-P=15000(1+\dfrac{16}{100})^3-20184=23413.44-20184=32.29.44$$-----------(ii)

From the equation (i) and (ii), the required difference

$$CI_2 - CI_1=3229.44-2784=445.44$$Rs.