Final answer:
The question asks for the Internal Rate of Return (IRR) on an investment using cash flows and the net present value (NPV) approach. The IRR is the interest rate that zeroes out the NPV of the investment's cash flows. To find the IRR, you would typically use an iterative approach or a financial calculator, as the equation cannot be easily solved algebraically.
Step-by-step explanation:
The student's question is focused on finding the Internal Rate of Return (IRR) for a series of cash flows from an investment. To calculate the IRR, one needs to set the net present value (NPV) of all cash flows to zero and solve for the annual effective interest rate (i).
In the provided scenario, Gemma invests $500 and receives $200 in one year and $400 in two years. We need to find the interest rate i that makes the NPV equation equal to zero: NPV = -500 + 200/(1+i) + 400/((1+i)^2) = 0. This equation cannot be solved algebraically, and requires either iterative methods or financial calculators to find the correct rate.
The concept of present value is crucial to understand here. Present value calculates the current worth of a future sum of money given a specific interest rate. The cash flows are then discounted back to the present day to assess an investment's profitability.