Final answer:
Using the compound interest formula, we find that the annual compound interest rate needed for Rs. 625 to grow to Rs. 729 in 2 years is 8%. Hence, option (a) is the correct answer.
Step-by-step explanation:
The question is asking to find the rate percent compound interest that would make an amount of Rs. 625 grow to Rs. 729 in 2 years. To solve this, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.
Since the interest is compounded annually, n = 1. We need to find r such that 729 = 625(1 + r)^2. This simplifies to (1 + r)^2 = 729/625, and therefore, 1 + r = √(729/625). Solving for r gives us r = √(729/625) - 1, which equals r = (27/25) - 1, thus r = 2/25 or r = 0.08. So the annual compound interest rate is 8%.
Therefore, the correct answer is: a. 8%