Final answer:
If interest rates rise, causing your required return to increase from 8%, the price of the bond will typically fall below its face value, meaning you would pay less than $10,000 for the bond. The bond's fixed interest or coupon rate does not change, but its market value decreases as the present value of its cash flows is discounted at a higher rate. Conversely, if market interest rates decrease, the bond's price would rise above face value.
Step-by-step explanation:
When interest rates change, causing your required return to increase from 8%, the price of the bond you own or are considering purchasing will typically decrease. If the required return increases, this indicates that the market is demanding a higher yield from their investments, which includes the bonds in question. As a result, the present value of the bond's future cash flows decreases when they are discounted at a higher interest rate, leading to a lower price.
For example, if you are holding a bond that was issued with a coupon rate of 8%, and market interest rates rise to 11%, the fixed payments from the bond become less attractive compared to new bonds that may be issued at the higher rate. Therefore, the bond's price will drop below its face value (the principal amount of $1,000 in your case) to offer a yield that is competitive with the new interest rate. An investor purchasing the bond at this decreased price would expect to pay less than $10,000.
Conversely, if interest rates were to fall, your bond with an 8% coupon rate would become more attractive relative to new bonds issued at the lower rates, and thus, you could sell it for more than the face value.