Question
What is the present value that Derek is willing to pay for the money machine today, given a 10% discount rate and a future payment of $47,368.00 in 13 years?
Answers
Answered by
GPT-4o mini
To find the present value (PV) that Derek is willing to pay for the money machine today, we can use the formula for present value:
\[
PV = \frac{FV}{(1 + r)^n}
\]
Where:
- \( FV \) is the future value (the amount of money in the future),
- \( r \) is the discount rate (as a decimal), and
- \( n \) is the number of years until the payment is received.
Given:
- \( FV = 47,368.00 \)
- \( r = 0.10 \) (10% discount rate)
- \( n = 13 \)
Now we can substitute the values into the formula:
\[
PV = \frac{47,368.00}{(1 + 0.10)^{13}}
\]
Calculating \( (1 + 0.10)^{13} \):
\[
(1.10)^{13} \approx 3.478
\]
Now we can compute the present value:
\[
PV = \frac{47,368.00}{3.478} \approx 13,609.21
\]
Therefore, the present value that Derek is willing to pay for the money machine today is approximately **$13,609.21**.
\[
PV = \frac{FV}{(1 + r)^n}
\]
Where:
- \( FV \) is the future value (the amount of money in the future),
- \( r \) is the discount rate (as a decimal), and
- \( n \) is the number of years until the payment is received.
Given:
- \( FV = 47,368.00 \)
- \( r = 0.10 \) (10% discount rate)
- \( n = 13 \)
Now we can substitute the values into the formula:
\[
PV = \frac{47,368.00}{(1 + 0.10)^{13}}
\]
Calculating \( (1 + 0.10)^{13} \):
\[
(1.10)^{13} \approx 3.478
\]
Now we can compute the present value:
\[
PV = \frac{47,368.00}{3.478} \approx 13,609.21
\]
Therefore, the present value that Derek is willing to pay for the money machine today is approximately **$13,609.21**.