Final answer:
If interest rates increase, you would expect to pay less than $10,000 for a bond worth that amount at issue due to the inverse relationship between bond prices and interest rates. A decrease in rates would have the opposite effect, potentially increasing the bond's price above $10,000.
Step-by-step explanation:
When considering the impact of interest rate changes on the price of a bond, the general relationship is inverse. This means that when interest rates rise, the price of existing bonds typically falls, and vice versa. Therefore, if interest rates increase, you would expect to pay less than $10,000 for a bond that was originally issued at $10,000 because its yield must increase to match the new, higher interest rates in the market, making it less valuable. Conversely, if interest rates decrease, the existing bond's yield is now higher than the market rate, making it more valuable, and you would expect to pay more than $10,000. The historical context provided by LibreTexts indicates that the federal government's interest payments on borrowing have fluctuated over time, affected by changes in interest rates and economic policies.