Final answer:
The price of a long-term bond, Bond A, will decrease more than that of a short-term bond, Bond B, if interest rates rise. Longer duration bonds are more sensitive to interest rate changes. A bond bought at a time when interest rates are higher than its coupon rate will cost less than its face value.
Step-by-step explanation:
If interest rates increase, the price of Bond A, which has 20 years to maturity, will generally decrease more than the price of Bond B, which has 5 years to maturity. This is due to the concept known as duration, which measures the sensitivity of a bond's price to changes in interest rates. Long-term bonds like Bond A have longer durations and are more sensitive to interest rate changes than short-term bonds like Bond B. Hence, if interest rates rise, long-term bond prices fall more significantly.
For example, 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 maturity, but the current interest rates are now 9%, you would expect to pay less than the face value of the bond because investors would require a higher yield to compensate for the higher prevailing interest rates. The actual price you'd be willing to pay would be less than $10,000 to achieve an effective yield that is competitive with the new 9% market rate.