A money lender borrows a sum at an annual simple interest rate of 4%, paying the interest at the year's end. He then lends this amount at a 6% annual compound interest rate, compounded semi-annually, and receives the interest after one year. If his profit at the end of the year is Rs 104.50, what is the principal amount he initially borrowed?

Explanation

Let the borrowed amount be Rs x. Interest paid by the lender at 4% simple interest for 1 year = x × (4/100) = x/25. Interest received from lending at 6% compound interest compounded half-yearly: Rate per half year = 6%/2 = 3% = 0.03. Amount after 1 year = x × (1 + 0.03)^2 = x × (1.03)^2 = x × 1.0609. Interest received = x × 1.0609 – x = 0.0609x. Profit = Interest received – Interest paid = 0.0609x – x/25 = 0.0609x – 0.04x = 0.0209x. Given profit = Rs 104.50, 0.0209x = 104.50 x = 104.50 / 0.0209 = 5000. Therefore, the amount borrowed is Rs 5000.