Final answer:
The expected selling price of a security in 3 years that pays an annual amount of $7,500 for 9 years using a discount rate of 7.5 percent can be found by calculating the present value of the annuity for the years 3 to 9 and discounting that amount back to the present.
Step-by-step explanation:
To calculate the expected selling price of a security that pays $7,500 per year for 9 years, with a discount rate of 7.5 percent, we will need to calculate the present value of the security's cash flows starting in year 3 and ending in year 9.
Since the security pays a consistent annual payment, we can use the present value annuity formula to find the value:
$P = PMT \times \left(\frac{1 - (1 + r)^{-n}}{r}\right)$
Where $P$ is the present value, $PMT$ is the annual payment, $r$ is the discount rate, and $n$ is the number of periods. To find the price in 3 years, we consider payments from year 3 to year 9 (a total of 7 payments).
Using the values $PMT = $7,500, $r = 0.075$, and $n = 7$, we calculate the present value worded value in year 3. We then have to discount this value back to the present (year 0) with 3 periods. This involves dividing the previously calculated present value by $(1 + r)^3$.