$Answer:$4000
Step-by-step explanation:
To calculate the present and future value of the investment for a specific year, you can use the concept of the time value of money. The present value (PV) represents the current worth of a future sum of money, while the future value (FV) represents the worth of that sum at a specified future date.
Let's calculate the present and future value for Year 3, which is $4,000.
1. Present Value (PV):
The present value of $4,000 in Year 3 can be calculated by discounting it back to the present using an appropriate discount rate. In this case, we assume a discount rate of 5%. The formula for present value is:
PV = FV / (1 + r)^n
Where:
- PV = Present Value
- FV = Future Value
- r = Discount rate per year (as a decimal)
- n = Number of years
PV = $4,000 / (1 + 0.05)^3
PV = $4,000 / (1.05)^3
PV ≈ $4,000 / 1.157625
PV ≈ $3,454.545 (rounded to the nearest dollar)
So, the present value of $4,000 in Year 3 is approximately $3,455.
2. Future Value (FV):
The future value of $4,000 in Year 3 can be calculated using the formula:
FV = PV * (1 + r)^n
Where:
- FV = Future Value
- PV = Present Value
- r = Interest rate per year (as a decimal)
- n = Number of years
In this case, we'll assume an interest rate of 5% per year.
FV = $3,455 * (1 + 0.05)^3
FV = $3,455 * (1.05)^3
FV ≈ $3,455 * 1.157625
FV ≈ $4,000 (rounded to the nearest dollar)
So, the future value of $4,000 in Year 3 is approximately $4,000.