2. If you have an opportunity cost of 10%, how much should you be willing to invest now to have $8,000 accumulated in 10 years?
To determine how much you should be willing to invest now to accumulate $8,000 in 10 years, we need to use the concept of present value.
The present value formula is:
PV = FV / (1 + r)^n
Where:
PV = Present Value
FV = Future Value
r = Interest Rate (also known as the opportunity cost)
n = Number of years
In this case, the Future Value (FV) is $8,000, the Number of years (n) is 10, and the Interest Rate (r) is 10%.
Now, we can substitute the values into the formula:
PV = 8000 / (1 + 0.1)^10
To calculate it:
PV = 8000 / (1.1)^10
PV = 8000 / 2.59374
PV ≈ $3,086.67
Therefore, you should be willing to invest approximately $3,086.67 now to have $8,000 accumulated in 10 years, considering an opportunity cost of 10%.