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.
To compute the present value of a cash flow, you need to use the formula for calculating present value:
PV = CF / (1 + r)^t
Where:
PV = Present Value
CF = Cash Flow
r = Discount rate
t = Time period
For problem 1:
a. To calculate the present value when r = 8% and t = 10 years, substitute the given values into the formula:
PV = $100 / (1 + 0.08)^10
b. To calculate the present value when r = 8% and t = 20 years, substitute the given values into the formula:
PV = $100 / (1 + 0.08)^20
c. To calculate the present value when r = 4% and t = 10 years, substitute the given values into the formula:
PV = $100 / (1 + 0.04)^10
d. To calculate the present value when r = 4% and t = 20 years, substitute the given values into the formula:
PV = $100 / (1 + 0.04)^20
For problem 2:
To compute the future value of a cash flow, you need to use the formula for calculating future value:
FV = CF * (1 + r)^t
Where:
FV = Future Value
CF = Cash Flow
r = Discount rate
t = Time period
Using the same combinations of rates and times as in problem 1, substitute the given values into the formula:
a. FV = $100 * (1 + 0.08)^10
b. FV = $100 * (1 + 0.08)^20
c. FV = $100 * (1 + 0.04)^10
d. FV = $100 * (1 + 0.04)^20
Once you substitute the numbers into the formulas, you can solve the equations to find the present value or future value for each combination of rates and times.