a. $24,000 x (1 + 0.08)^3 = $32,768 b. $24,000 x (1 + 0.08)^6 = $45,158.72 c. $24,000 x (1 + 0.08)^9 = $60,977.56 d. $24,000 x (1 + 0.08)^12 = $81,302.97

a. $120,000 / (1 + 0.03)^5 = $90,829.51 b. $120,000 / (1 + 0.06)^5 = $81,717.66 c. $120,000 / (1 + 0.09)^5 = $73,968.43 d. $120,000 / (1 + 0.12)^5 = $67,382.23

- To calculate the internal rate of return or IRR for the project, we need to find the discount rate that makes the net present value (NPV) of the expected cash flows equal to zero. The formula for NPV is:

NPV = -C0 + (C1 / (1 + r)^1) + (C2 / (1 + r)^2) + (C3 / (1 + r)^3) + (C4 / (1 + r)^4) + (C5 / (1 + r)^5)

Where C0 is the initial investment, C1, C2, C3, C4, C5 are the expected cash flows for each year, and r is the discount rate or IRR.

- To calculate the net present value (NPV), we will use the formula:

NPV = (-C0) + (C1 / (1 + r)^1) + (C2 / (1 + r)^2) + (C3 / (1 + r)^3) + (C4 / (1 + r)^4) + (C5 / (1 + r)^5)

Where C0 is the initial investment ($900,000), C1, C2, C3, C4, C5 are the expected cash flows for each year ($120,000, $155,000, $186,000, $208,000, and $225,000 respectively), and r is the discount rate (10%).

NPV = (-900,000) + (120,000 / (1 + 0.1)^1) + (155,000 / (1 + 0.1)^2) + (186,000 / (1 + 0.1)^3) + (208,000 / (1 + 0.1)^4) + (225,000 / (1 + 0.1)^5)

NPV = -900,000 + 108,333 + 125,500 + 153,286 + 185,185 + 190,476

NPV = 1,042,770

If the NPV is positive, the project will generate more value than the cost of the investment, and it is recommended to proceed with the project.

- Payback period is the amount of time required to recover the initial investment of a project. To calculate the payback period, we will sum up the cash flows until they exceed the initial investment of $900,000.

Year 1: $120,000 Year 2: $120,000 + $155,000 = $275