To calculate the present value (PV) of a future amount of money, we use the formula:
PV = FV / (1 + r)^n
Where:
- PV = Present Value
- FV = Future Value ($1,000 in this case)
- r = Discount rate (as a decimal)
- n = Number of years until the money is received (5 years here)
Given:
- FV = $1,000
- r = 12.78% = 0.1278
- n = 5
Substituting the values into the formula:
PV = 1000 / (1 + 0.1278)^5
This simplifies to:
PV = 1000 / (1.1278)^5
Calculating the value of (1.1278)^5:
1.1278^5 ≈ 1.719
Now, substituting that back into the equation:
PV = 1000 / 1.719
Thus:
PV ≈ $581.77
Therefore, the present value of $1,000 to be received in 5 years, with a discount rate of 12.78%, is approximately $581.77.