Final answer:
The present value of an 8-year annuity with annual payments of $3,000 at a 9 percent interest rate depends on the present value formula. The present value rises as interest rates drop and falls as they rise, demonstrating the interest rate risk and reflecting the concept of opportunity cost.
Step-by-step explanation:
The student has asked about the relationship between the present value of an annuity and interest rates. As interest rates drop, the present value of an annuity increases, and as interest rates rise, the present value decreases. When it comes to the future value of an annuity, the opposite is true; it decreases as interest rates drop.
Given an 8-year annuity at a 9 percent interest rate with annual payments of $3,000, the present value of this investment would be calculated using the formula for the present value of an ordinary annuity. Unfortunately, without performing the actual calculation, which involves a mathematical formula, the exact present value cannot be provided.
The understanding of how the present value changes is key in investments like bonds, which carry interest rate risk. For example, a bond purchased at an 8% interest rate would see its present value decrease if the market interest rate were to increase to 12%, since new bonds now offer a higher return. This also illustrates the concept of opportunity cost in finance.