Determine the present values if $5,000 is received in the future (at the end of each indicated time period) in each of the following situations:
a. 5% for 10yrs
b. 7% for 7yrs
c. 9% for 4yrs
I will do the last one, you do the other two in the same way
c)
PV = 5000(1.09)^-4
= $3542.13
To determine the present value in each situation, we will use the formula for calculating the present value of a future amount.
The formula for calculating the present value (PV) of a future amount (FV) is:
PV = FV / (1 + r)^n
Where:
PV = Present value
FV = Future value
r = Interest rate
n = Number of time periods
a. Situation a: 5% for 10 years
PV = 5,000 / (1 + 0.05)^10
PV = 5,000 / (1.05)^10
PV = 5,000 / 1.6289
PV ≈ 3,072.44
b. Situation b: 7% for 7 years
PV = 5,000 / (1 + 0.07)^7
PV = 5,000 / (1.07)^7
PV = 5,000 / 1.5038
PV ≈ 3,325.66
c. Situation c: 9% for 4 years
PV = 5,000 / (1 + 0.09)^4
PV = 5,000 / (1.09)^4
PV = 5,000 / 1.4116
PV ≈ 3,541.13
Therefore, the present values in each situation are approximately:
a. $3,072.44
b. $3,325.66
c. $3,541.13