The simple interest on a certain principal for 3 years at an annual rate of 8% is equal to half the compound interest earned on Rs. 4000 over 2 years at 10% per annum. What is the principal amount invested at simple interest?

Explanation

First, calculate the compound interest on Rs. 4000 for 2 years at 10% per annum: CI = 4000 * (1 + 0.10)^2 - 4000 = 4000 * 1.21 - 4000 = Rs. 840. Since the simple interest is half of this, SI = 840 / 2 = Rs. 420. Using the simple interest formula SI = (P * R * T) / 100, we get 420 = (P * 8 * 3) / 100, which simplifies to P = (420 * 100) / (3 * 8) = Rs. 1750.