Final answer:
Changes in market interest rates inversely affect bond prices; a bond's price will be lower than par if interest rates rise above the bond's coupon rate, and higher if interest rates fall below the coupon rate. Applying this principle, if market interest rates rise, one would pay less than the par value for a bond.
Step-by-step explanation:
The subject of this question is related to Business, specifically financial mathematics and the valuation of bonds. When determining whether you would expect to pay more or less than $10,000 for a bond, given the change in market interest rates, it is important to consider the relationship between bond prices and interest rates. If the market interest rate (Yield to Maturity, or YTM) is higher than the bond's coupon rate, the bond's price will be lower than its par value; conversely, if the market interest rate is lower, the bond's price will be higher.
For example, if a local water company issued a $10,000 ten-year bond at 6% interest, and the market interest rate increased to 9% one year before the end of the ten years, you would expect to pay less than $10,000 for the bond. This is because the bond’s coupon payments are less attractive compared to the new, higher market rates, causing its price to drop so that its yield to maturity increases to the new market level of 9%.
If we calculate the bond's price when its coupon interest rate is less than the market interest rate, such as a bond paying $1,080 (final coupon and principal repayment) one year from now, we can see if 12% is the current market rate, and we can obtain $1,080 from an alternative investment by investing $964 ($964 * 1.12 = $1,080), then we would not be willing to pay more than $964 for the original $1,000 bond. This shows us how changes in market rates affect bond prices inversely and demonstrates the concept of present value and discounting future cash flows.