Final answer:
The maximum amount you would be willing to invest today to receive $10,000 in 21 years at a 2.875% return is approximately $5539.59.
Step-by-step explanation:
To determine the most a student would be willing to spend on an investment that will pay $10,000 at the end of 21 years with a required return of 2.875%, we use the present value formula for a single future amount:
Present Value (PV) = Future Value (FV) / (1 + r)^n
Where:
- FV is the future value of the investment, which is $10,000.
- r is the annual interest rate (as a decimal), which is 2.875% or 0.02875.
- n is the number of years until the investment matures, in this case, 21 years.
Substituting the values into the formula gives us:
PV = $10,000 / (1 + 0.02875)^21
Calculating this gives:
PV = $10,000 / (1.02875)^21
PV = $10,000 / 1.80575
PV = $5539.59 (approx.)
Therefore, the maximum amount you would be willing to invest today to have $10,000 in 21 years, given a 2.875% annual return, is approximately $5539.59.
This amount reflects the time value of money, which recognizes that money available now is worth more than the identical sum in the future due to its potential earning capacity.