what is the present value of a security that will pay $5,000 in 20 rears if securities of equal risk pay 7% annually?

To determine the present value of a future sum, we use the concept of present value, which accounts for the time value of money. The present value formula is:

Present Value = Future Value / (1 + interest rate)^n

Where:
- Future Value is the amount you will receive in the future ($5,000 in this case)
- Interest rate is the annual rate of return (7% or 0.07 as a decimal)
- n is the number of periods (20 years in this case)

Now let's calculate the present value step by step:

1. Convert the interest rate to decimal form:
Interest rate = 7% = 0.07

2. Plug the values into the formula:
Present Value = $5,000 / (1 + 0.07)^20

3. Calculate the term inside the parentheses first:
(1 + 0.07)^20 = 2.653297...

4. Divide the Future Value by the term calculated in step 3:
Present Value = $5,000 / 2.653297... ≈ $1,884.49

Therefore, the present value of a security that will pay $5,000 in 20 years, with securities of equal risk paying 7% annually, is approximately $1,884.49.