A certain sum amounts to Rs. 7000 in 2 years and to Rs. 8000 in 3 years. Find…

Solution: Use compound interest relations to find the principal.

1. Let P be the principal and r the annual compound interest rate (in decimal).

2. After 2 years: P(1+r)^2 = 7000. After 3 years: P(1+r)^3 = 8000.

3. Divide the 3-year amount by the 2-year amount to eliminate P: (1+r) = 8000/7000 = 8/7, so r = 1/7.

4. Now find P: P = 7000/(1+r)^2 = 7000/(8/7)^2 = 7000 * (49/64) = 5359.375.

5. Therefore, the required sum (principal) is Rs 5359.375.