Final answer:
To find the price one would pay for an investment offering annual payments and a lump sum at maturity, we calculate the present values of both components and sum them. Using the present value formulas for an annuity and a single sum with the given 8% interest rate, the total present value is approximately $546,319.84, so option d. $546,317 is the closest answer.
Step-by-step explanation:
To determine what one would pay for an investment that pays $40,000 at the end of each year for the next ten years, plus a maturity value of $600,000 after ten years, with an 8% interest rate, we must calculate the present value of an annuity plus the present value of a single sum. The formula to calculate the present value of an annuity is PV = PMT × ((1 - (1 + r)^{-n}) / r), where PMT is the annual payment ($40,000), r is the interest rate (0.08), and n is the number of periods (10). Additionally, the formula for the present value of a single sum is PV = FV / (1 + r)^n, where FV is the future value ($600,000), r is the interest rate (0.08), and n is the number of periods (10). Applying these formulas:
- Present Value of the Annuity (PMT): 40,000 × ((1 - (1 + 0.08)^{-10}) / 0.08) = 40,000 × 6.71008 = $268,403.2
- Present Value of the Maturity Value (FV): 600,000 / (1 + 0.08)^{10} = $600,000 / 2.15892 = $277,916.64
- Total present value: $268,403.2 (Annuity PV) + $277,916.64 (Maturity PV) = $546,319.84
Therefore, the closest answer to the total present value of the investment is option d. $546,317.