Final answer:
To find the present value of annuity payments, use the present value of annuity formula for periods of 15, 40, and 75 years, and the perpetual annuity formula for infinite payments. Both calculations require the given payment amount and 8% interest rate, not the 15% or 25% rates from the examples.
Step-by-step explanation:
The question requires calculating the present value of annuity payments for 15 years, 40 years, 75 years, and in perpetuity, assuming an 8 percent required rate of return. To calculate the present value for a finite number of periods (15, 40, or 75 years), we use the present value of annuity formula:
PV = PMT × (1 - (1 + r)^-n) / r
Where PV is present value, PMT is the annual payment ($6,125), r is the annual interest rate (0.08), and n is the number of periods (15, 40, or 75 years). For the perpetual annuity, we use the formula:
PV = PMT / r
This formula does not factor in the number of periods since it's assumed to go on indefinitely. To find the value of the investment for each scenario, one would perform these calculations with the respective values substituted in.
Please note the annuity payments are given at an 8% rate, while the provided examples use different interest rates (15% and 25%) which do not apply to this scenario directly but indicate the process of discounting future cash flows to their present value.