To calculate the present value (PV) of $100 to be received in 10 years, we can use the present value formula:
PV = FV / (1 + r)^n
Where:
- PV = Present Value
- FV = Future Value (the amount to be received in the future)
- r = discount rate (opportunity cost)
- n = number of years until payment
In this case, the future value (FV) is $100, the discount rate (r) is 9% or 0.09, and the number of years (n) is 10.
Plugging in the values:
PV = 100 / (1 + 0.09)^10
This simplifies to:
PV = 100 / (1.09)^10
Calculating (1.09)^10 gives us approximately 2.367:
PV = 100 / 2.367
Therefore, the present value is approximately:
PV ≈ $42.34
This means that if you want to have $100 in 10 years, you would need to invest approximately $42.34 today at a 9% return rate. This calculation helps illustrate how much future cash flows are worth in today’s terms, considering the opportunity cost of capital.