Final answer:
To calculate the present value of an annuity of $4,500 per year, we use the present value of an annuity formula and then adjust the calculation for the fact that the first payment is received 7 years from today. We then discount this value back to today's value at an 8% discount rate.
Step-by-step explanation:
To find the present value of $4,500 per year at a discount rate of 8 percent, with the first payment received 7 years from today and the last payment received 25 years from today, we use the present value of an annuity formula:
PV = Pmt * [(1 - (1 + r)^(-n)) / r]
Where:
- PV is the present value of the annuity
- Pmt is the annual payment ($4,500)
- r is the discount rate (0.08)
- n is the total number of payments (25 - 7 + 1 = 19 years of payments)
However, we must first discount the entire annuity back 6 years, since the first payment starts 7 years from today:
PV = $4,500 * [(1 - (1 + 0.08)^(-19)) / 0.08]
Calculate this value and then discount it back 6 years using the formula:
PV_{today} = PV / (1 + 0.08)^6
After finding the present value of the annuity, we can discount it further to find the value today.