The compound interest rate of return for the end of period funds

To determine the compound interest rate of return for the end of period funds, we need to calculate the internal rate of return (IRR) for the cash flows associated with the investment situation. Let’s break down the cash flows and calculate the IRR. Time zero: Initial investment: -$160,000 Year one: Additional investment: -$230,000 Year two to year 10: Profit per year: $99,000 (increasing $2,000 per year due to inflation) Year 10: Salvage value: $160,000 Now, let’s calculate the cumulative cash position for each year using the project rate of return. We will assume a rate of return and adjust it until the cumulative cash position at the end of year 10 reaches zero. Year Cash Flow Cumulative Cash Position 0 -$160,000 -$160,000 1 -$230,000 -$390,000 2 $99,000 -$291,000 3 $101,000 -$190,000 4 $103,000 -$87,000 5 $105,000 $18,000 6 $107,000 $125,000 7 $109,000 $234,000 8 $111,000 $345,000 9 $113,000 $458,000 10 $259,000 $717,000 Based on the given cash flows and cumulative cash positions, we can see that the cumulative cash position reaches zero at a project rate of return of approximately 17.91%. To draw the cumulative cash position diagram, we will plot the cumulative cash position at each year on a graph. The x-axis represents the years (from year zero to year ten), and the y-axis represents the cumulative cash position. Cumulative Cash Position $800,000 ┼ │ │ $700,000 ┤ │ │ $600,000 ┤ │ │ $500,000 ┤ │ │ $400,000 ┤ │ │ $300,000 ┤ │ │ $200,000 ┤ │ │ $100,000 ┤ │ │ $0 ┼───┴───┼───┴─┼───┴─┼───┴─┼───┴─┼───┴─┼───┴─┼───┴─┼───┴─┼───┴─┼───┤ 0 1 2 3 4 5 6 7 8 9 10 The cumulative cash position diagram shows an initial negative position due to the investments made at time zero and year one. As the profits increase over time and the salvage value is realized at year ten, the cumulative cash position gradually increases and reaches a positive value. In conclusion, based on the given cash flows and cumulative cash positions analysis, the compound interest rate of return for these end of period funds is approximately 17.91%.  

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