1. Present Values. Compute the present value of a $100 cash flow for the following combinations of discount rates and times.

a. r = 8 percent. t = 10 years
b. r = 8 percent. t = 20 years
c. r = 4 percent. t = 10 years
d. r = 4 percent. t = 20 years

2. Future Values: Compute the future value of a $100 cash flow for the same combinations of rates and times as in problem 1.

1. a. To compute the present value of a $100 cash flow after 10 years with a discount rate of 8 percent, I would grab my calculator...or my magic wand and perform some calculations. The present value would be approximately $46.55. Not bad, right?

b. Now, let's fast forward to 20 years in the future, still with a discount rate of 8 percent. The present value of that $100 cash flow would be around $30.17. It's starting to feel like time travel, isn't it?

c. If we lower the discount rate to 4 percent but keep the time frame at 10 years, the present value of that $100 cash flow would be about $67.56. Hey, at this rate, I might just invest in a time machine!

d. Lastly, let's switch to a discount rate of 4 percent and extend the time period to 20 years. The present value of that $100 cash flow would be roughly $54.30. Time flies, but luckily cash flows don't!

2. Alright, let's move on to future values now. We have the same combinations of rates and times as in problem 1:

a. With a discount rate of 8 percent and a time frame of 10 years, the future value of that $100 cash flow would be approximately $215.89. That's enough to buy everyone in the office a clown nose!

b. Fast forward to 20 years with a discount rate of 8 percent, and the future value of that $100 cash flow would be roughly $466.10. I hope you're prepared to throw a massive party!

c. Lowering the discount rate to 4 percent but keeping the time frame at 10 years, the future value of that $100 cash flow would be around $148.02. Looks like the circus just came to town!

d. Lastly, let's switch to a discount rate of 4 percent and extend the time period to 20 years. The future value of that $100 cash flow would be approximately $221.76. Looks like we've landed in the future... and it's full of laughter!

1. To compute the present value of a $100 cash flow, you can use the formula:

PV = CF / (1 + r)^t

where PV is the present value, CF is the cash flow, r is the discount rate, and t is the time.

a. For r = 8 percent and t = 10 years:

PV = 100 / (1 + 0.08)^10
PV = 100 / (1.08)^10
PV ≈ 46.80

b. For r = 8 percent and t = 20 years:

PV = 100 / (1 + 0.08)^20
PV = 100 / (1.08)^20
PV ≈ 21.72

c. For r = 4 percent and t = 10 years:

PV = 100 / (1 + 0.04)^10
PV = 100 / (1.04)^10
PV ≈ 67.56

d. For r = 4 percent and t = 20 years:

PV = 100 / (1 + 0.04)^20
PV = 100 / (1.04)^20
PV ≈ 54.29

2. To compute the future value of a $100 cash flow, you can use the formula:

FV = CF * (1 + r)^t

where FV is the future value, CF is the cash flow, r is the interest rate, and t is the time.

Using the same combinations as in problem 1:

a. For r = 8 percent and t = 10 years:

FV = 100 * (1 + 0.08)^10
FV = 100 * (1.08)^10
FV ≈ 215.89

b. For r = 8 percent and t = 20 years:

FV = 100 * (1 + 0.08)^20
FV = 100 * (1.08)^20
FV ≈ 466.09

c. For r = 4 percent and t = 10 years:

FV = 100 * (1 + 0.04)^10
FV = 100 * (1.04)^10
FV ≈ 148.02

d. For r = 4 percent and t = 20 years:

FV = 100 * (1 + 0.04)^20
FV = 100 * (1.04)^20
FV ≈ 219.11

To compute the present value and future value of a cash flow, you will need to use the formulas for present value (PV) and future value (FV).

1. Present Values:
a. To calculate the present value of a $100 cash flow with a discount rate (r) of 8 percent and a time (t) of 10 years, you can use the formula for present value: PV = FV / (1 + r)^t. Plugging in the values, you get PV = $100 / (1 + 0.08)^10.

b. To calculate the present value with the same cash flow and a time of 20 years, you can use the same formula as before: PV = $100 / (1 + 0.08)^20.

c. To calculate the present value with a 4 percent discount rate and a time of 10 years, use the present value formula: PV = $100 / (1 + 0.04)^10.

d. To calculate the present value with the same variables but a time of 20 years, use the same formula as before: PV = $100 / (1 + 0.04)^20.

2. Future Values:
a. To compute the future value of a $100 cash flow with a discount rate of 8 percent and a time of 10 years, use the formula for future value: FV = PV * (1 + r)^t. Plugging in the values, you get FV = $100 * (1 + 0.08)^10.

b. To compute the future value with the same cash flow and a time of 20 years, use the same formula as before: FV = $100 * (1 + 0.08)^20.

c. To compute the future value with a discount rate of 4 percent and a time of 10 years, use the future value formula: FV = $100 * (1 + 0.04)^10.

d. To compute the future value with the same variables but a time of 20 years, use the same formula as before: FV = $100 * (1 + 0.04)^20.

By substituting the appropriate values into these equations, you should be able to compute the present and future values for each combination of discount rates and times.