Final answer:
The 15-year bond would have a larger increase in price compared to the 10-year bond when interest rates drop from 10% to 5%, due to its longer duration and higher sensitivity to interest rate changes.
Step-by-step explanation:
If the rates on a 15 year and 10 year bond each went from 10% to 5%, the bond with the longer duration, which in this case is the 15-year bond, would have a larger increase in price. This is because the longer-duration bonds are more sensitive to changes in interest rates, as they have a longer period of time before maturity to collect the now higher-than-market coupon payments. When interest rates decrease, existing bonds with higher rates become more valuable since new bonds are being issued at the lower current rate.
In the example given, both a 15-year and a 10-year bond have witnessed a drop in interest rates from 10% to 5%. Therefore, both bonds will increase in value. However, because the 15-year bond promises longer-term coupon payments at the old higher rate, its value will increase more compared to the 10-year bond.
The par value mentioned does not directly influence the relative change in price due to interest rate movements, but it does serve as the face value of the bonds. If the interest rates decline as described, investors would expect to pay more than the $1,000 par value for each bond, because the fixed $100 payment represents a higher yield relative to the new market interest rate of 5%.