Final answer:
Bond prices fall when interest rates rise, with longer maturity bonds being more sensitive to rate changes. The prices provided correspond to the bonds in a way that reflects this sensitivity, with the lowest price likely belonging to the bond with the longest maturity.
Step-by-step explanation:
The question provided involves understanding the relationship between bond prices, interest rates, and maturity. When interest rates rise, the price of existing bonds generally falls because their fixed coupon payments are less attractive compared to the new bonds issued at higher rates. However, the impact of interest rate changes on bond prices is more significant for bonds with longer maturities.
For bonds with face values of $1,000 and coupon rates of 8% but with different maturities (2, 10, and 20 years), the bond prices when the interest rates increase to 10% will vary. The longer the maturity of a bond, the more sensitive its price is to interest rate changes. This means that, all else being equal, the bond with the 20-year maturity will experience the greatest drop in price, followed by the 10-year bond, and then the 2-year bond.
In this case, the bond with the lowest price of $828.36 is likely the one with the longest maturity (20 years), as it is the most sensitive to the interest rate rise. The bond priced at $964.54 is likely the one with the next longest maturity (10 years), and the bond priced at $875.39 is likely the 2-year bond, as it would be least affected by the interest rate hike.