Final answer:
The present value of a security that will pay $16,000 in 20 years at an annual interest rate of 9% is approximately $2,973.64. The present value is calculated using the formula PV = FV / (1 + r)^n.
Step-by-step explanation:
The present value of a security that will pay $16,000 in 20 years, given that the securities of equal risk pay a 9% annual interest rate, can be calculated using the present value formula: PV = FV / (1 + r)^n, where PV is the present value, FV is the future value, r is the annual interest rate, and n is the number of years.
In this case, the future value (FV) is $16,000, the annual interest rate (r) is 9% or 0.09, and the number of years (n) is 20. The calculation would, therefore, be: PV = $16,000 / (1 + 0.09)^20.
After computing this, the present value (PV) would be approximately $2,973.64 (not rounded to nearest cent here for example purposes). To find the precise present value, do the calculation with a calculator and then round to the nearest cent.