To find out how much Derek is willing to pay for the money machine today, we need to calculate the present value (PV) of the future cash flow of $20,249.00 received in 9 years, discounted at a rate of 10.00%.
The formula for calculating the present value of a future cash flow is:
\[ PV = \frac{FV}{(1 + r)^n} \]
Where:
- \( PV \) = Present Value
- \( FV \) = Future Value ($20,249.00)
- \( r \) = discount rate (10% or 0.10)
- \( n \) = number of years until the cash flow is received (9 years)
Now, we can plug in the values:
\[ PV = \frac{20249}{(1 + 0.10)^9} \] \[ PV = \frac{20249}{(1.10)^9} \]
First, calculate \( (1.10)^9 \):
\[ (1.10)^9 \approx 2.3579477 \]
Now, substitute this value back into the present value formula:
\[ PV = \frac{20249}{2.3579477} \approx 8585.70 \]
Thus, the present value of the money machine is approximately $8,585.70.
Therefore, Derek should be willing to pay about $8,585.70 for the money machine today.
1 answer