Final answer:
The present value of a security that will pay $15,000 in 15 years at a 15% annual interest rate is found using the present value formula. After calculations, the present value is approximately $1,843.26.
Step-by-step explanation:
The present value of a security that will pay $15,000 in 15 years when securities of equal risk pay 15% annually is calculated using the present value formula: PV = FV / (1 + r)^n,
where,
PV = Present Value
FV = Future Value
r = Interest rate (decimal)
n = Number of periods
In this case, FV = $15,000, r = 0.15 (15% interest rate), and n = 15 years. Applying the formula, we get:
PV = $15,000 / (1 + 0.15)^15
PV = $15,000 / (1.15)^15
PV = $15,000 / 8.1377
PV = $1,843.26 approximately
Thus, the present value of the security is approximately $1,843.26.