Final answer:
If long-term rates rise above the bond's interest rate, the bond will sell at a discount. For example, a bond issued at a 6% interest rate would be worth less a year before maturity if the market rates increased to 9%, and you would pay less than its face value. Option d.
Step-by-step explanation:
If you own a 7% bond maturing in twenty years, and long-term rates increase to 10%, your bond would sell at a discount. This is because investors can get a better rate of return elsewhere, making your bond less attractive.
Therefore, the price of your bond must decrease to offer a similar yield to market rates. Conversely, a bond's price moves inversely to yield.
Let's examine a similar example to understand this concept better. Imagine a local water company issued a $10,000 ten-year bond at an interest rate of 6%. If you are considering buying this bond one year before the ten years are up, but interest rates have risen to 9%, you would expect to pay less than $10,000 for the bond.
To calculate what you would actually be willing to pay:
First, find out how much interest the bond will pay in the final year, which is 6% of $10,000, equal to $600.
Add the interest to the face value of the bond ($10,000 + $600 = $10,600), which is what you would receive at maturity.
Then, discount that amount back to its present value using the current 9% market rate. The formula for the present value of a future sum is PV = FV / (1 + r)^n, where FV is the future value ($10,600), r is the market interest rate (0.09), and n is the number of periods (1 year).
Calculate the present value: PV = $10,600 / (1 + 0.09)^1 = $10,600 / 1.09 ≈ $9,724.77
So, you would be willing to pay approximately $9,724.77 for this bond.