Final answer:
Using the present value formula, which considers the future value of the investment, the interest rate, and the time period, the most you should invest today for a future payment of $23,202 in 17 years at an 11.27% interest rate is $5,224.03.
Step-by-step explanation:
To find the most you should be willing to invest today for a future payment, you can use the present value formula, which is derived from the concept of compound interest. The present value (PV) formula is:
PV = FV / (1 + r)^n
Where:
- PV is the present value,
- FV is the future value or the amount the investment will pay in the future,
- r is the interest rate (expressed as a decimal), and
- n is the number of periods until payment.
Given that the future value (FV) is $23,202, the interest rate (r) is 11.27% (or 0.1127 as a decimal), and the number of periods (n) is 17 years, the calculation is:
PV = $23,202 / (1 + 0.1127)^17
Calculating this, we get:
PV = $23,202 / (1 + 0.1127)^17
PV = $23,202 / (1 + 0.1127)^17
PV = $23,202 / (4.439516)
PV = $5,224.03
Therefore, the most you should be willing to invest today is $5,224.03.