To determine how much Derek is willing to pay for the money machine today, we need to calculate the present value (PV) of the future payment he will receive. The formula for calculating the present value of a future payment is:
\[ PV = \frac{FV}{(1 + r)^n} \]
where:
- \( PV \) is the present value,
- \( FV \) is the future value,
- \( r \) is the discount rate,
- \( n \) is the number of years until payment.
Substituting the given values into the formula:
- \( FV = 14,068.00 \)
- \( r = 0.06 \) (which is 6%)
- \( n = 20 \)
The calculation is as follows:
\[ PV = \frac{14,068.00}{(1 + 0.06)^{20}} \] \[ PV = \frac{14,068.00}{(1.06)^{20}} \] \[ PV = \frac{14,068.00}{3.207135472} \] \[ PV \approx 4,381.48 \]
Therefore, Derek should be willing to pay approximately $4,381.48 for the money machine today.
1 answer