Kevin spends $4,000 for an investment that generates a continuous income stream at the rate of f₁(t) = 3,000 dollars per year. His friend, Molly, makes a separate investment that also generates income continuously, but at a rate of f₂(t) = 2,000e^0.04t dollars per year. The couple discovers that their investments have exactly the same net value over a 4-year period. If the prevailing annual interest rate stays fixed at 5% compounded continuously, how much did Molly pay for her investment?