Determine the present value (PV) now of an investment of $3,000 made one year from now and an additional $3,000 made two years from now if the annual discount rate is 4 percent.

Question

Determine the present value (PV) now of an investment of $3,000 made one year from now and an additional $3,000 made two years from now if the annual discount rate is 4 percent.

Answer 1

To determine the present value (PV) of an investment, we need to calculate the discounted value of future cash flows. In this case, we have two cash flows: $3,000 to be received one year from now and an additional $3,000 to be received two years from now. The discount rate is given as 4 percent.

The formula to calculate the present value (PV) is:

PV = FV / (1 + r)^n

Where:
PV = Present Value
FV = Future Value
r = discount rate
n = number of periods

Let's calculate the present value (PV) for each cash flow:

For the first cash flow of $3,000 received one year from now, n = 1:
PV1 = $3,000 / (1 + 0.04)^1

For the second cash flow of $3,000 received two years from now, n = 2:
PV2 = $3,000 / (1 + 0.04)^2

Now let's perform the calculations:

PV1 = $3,000 / (1 + 0.04)^1
= $3,000 / (1.04)^1
= $3,000 / 1.04
= $2,884.62 (rounded to two decimal places)

PV2 = $3,000 / (1 + 0.04)^2
= $3,000 / (1.04)^2
= $3,000 / 1.0816
= $2,773.09 (rounded to two decimal places)

Finally, to find the present value (PV) now of the investment, we need to sum up the present values of the two cash flows:

PV = PV1 + PV2
= $2,884.62 + $2,773.09
= $5,657.71 (rounded to two decimal places)

Therefore, the present value (PV) now of the investment is approximately $5,657.71.

Answer 2

To determine the present value (PV) of an investment, you can use the formula:

PV = CF1 / (1+r)^1 + CF2 / (1+r)^2

Where:
PV = Present Value
CF1 = Cash flow received in Year 1 (in this case, $3,000)
CF2 = Cash flow received in Year 2 (in this case, $3,000)
r = Discount rate (in this case, 4% or 0.04)

Let's calculate it step-by-step:

Step 1: Calculate the present value of cash flow received in Year 1:

PV1 = CF1 / (1+r)^1
= $3,000 / (1+0.04)^1
= $3,000 / (1.04)
= $3,000 / 1.04
= $2,884.62

Step 2: Calculate the present value of cash flow received in Year 2:

PV2 = CF2 / (1+r)^2
= $3,000 / (1+0.04)^2
= $3,000 / (1.04)^2
= $3,000 / 1.0816
= $2,770.78

Step 3: Calculate the total present value by summing up the present value of both cash flows:

PV = PV1 + PV2
= $2,884.62 + $2,770.78
= $5,655.40

Therefore, the present value (PV) of the investment is $5,655.40.

Answer 3

PV = 3000(1.04)^-1 + 3000(1.04)^-2

= ...