Determine the present value now of an investment of $3,000 made one one year from now and an additional $3,000 made two years from now if the annual discount rate is 4 percent.
PV = 3000(.96) + 3000(.96)^2
or
PV = 3000(1/04)^-1 + 3000(1.04)^-2
depending on how "annual discount rate" is defined in your course.
btw, they yield different results.
To determine the present value of future cash flows, we need to discount them back to the present using the given discount rate. In this case, the discount rate is 4 percent.
Step 1: Calculate the present value of the first cash flow ($3,000) made one year from now.
To calculate the present value, we use the formula: PV = FV / (1 + r)^n,
where PV is the present value, FV is the future value, r is the discount rate, and n is the number of periods.
In this case, PV = $3,000 / (1 + 0.04)^1 = $2,884.62 (rounded to two decimal places).
Step 2: Calculate the present value of the second cash flow ($3,000) made two years from now.
Using the same formula, PV = $3,000 / (1 + 0.04)^2 = $2,770.66 (rounded to two decimal places).
Step 3: Calculate the total present value.
Since the cash flows are occurring in different years, we need to sum up their present values.
Total present value = Present value of the first cash flow + Present value of the second cash flow
Total present value = $2,884.62 + $2,770.66 = $5,655.28 (rounded to two decimal places).
Therefore, the present value of the investment of $3,000 made one year from now and an additional $3,000 made two years from now, with a 4 percent annual discount rate, is approximately $5,655.28.
To determine the present value of the investment, we need to calculate the present value of each cash flow separately and then sum them up.
Let's calculate the present value of the $3,000 investment made one year from now first.
Step 1: Calculate the discount factor for year one.
Discount Factor = 1 / (1 + Discount Rate)^Number of Years
Discount Factor = 1 / (1 + 0.04)^1
Discount Factor = 1 / (1.04)
Discount Factor ≈ 0.9615
Step 2: Calculate the present value of the investment made one year from now.
Present Value = Cash Flow * Discount Factor
Present Value = $3,000 * 0.9615
Present Value ≈ $2,884.62
Next, let's calculate the present value of the $3,000 investment made two years from now.
Step 1: Calculate the discount factor for year two.
Discount Factor = 1 / (1 + Discount Rate)^Number of Years
Discount Factor = 1 / (1 + 0.04)^2
Discount Factor = 1 / (1.04^2)
Discount Factor ≈ 0.9246
Step 2: Calculate the present value of the investment made two years from now.
Present Value = Cash Flow * Discount Factor
Present Value = $3,000 * 0.9246
Present Value ≈ $2,773.80
Finally, let's sum up the present values of both investments.
Total Present Value = Present Value of Investment 1 + Present Value of Investment 2
Total Present Value = $2,884.62 + $2,773.80
Total Present Value ≈ $5,658.42
Therefore, the present value of the investment is approximately $5,658.42.