Final answer:
Gustavo should calculate the present value of the annual payments and the lump sum at an 8% discount rate and sum them to determine the maximum price he should pay for the investment.
Step-by-step explanation:
To calculate the maximum price Gustavo should pay for the investment given an 8% opportunity cost, we need to calculate the present value of both the annual payments of $2,400 for 9 years and the lump sum payment of $34,296 at the end of the 9th year. The formula for the present value of an annuity (annual payments) is PV = PMT [(1 - (1 + r)^-n) / r], where PMT is the amount paid per period (here, $2,400), r is the discount rate (here, 0.08), and n is the number of periods (here, 9).
The present value of the lump sum payment is calculated simply by discounting it back 9 years at the rate of 8%. Therefore, the present value (PV) of the lump sum is computed as PV = FV / (1 + r)^n, where FV is the future value (here, $34,296), r is the discount rate (here, 0.08), and n is the number of periods (here, 9).
To find the maximum amount Gustavo should be willing to pay for the investment, we sum up these two present values.