Explanation

This question involves understanding bond price behavior when interest rates change and the bond approaches maturity.

Key Information:

• Par value: $100
• Coupon rate: 7% (annual payments)
• Original discount rate: 6.5%
• Original price: $102.08 (premium bond since coupon rate > discount rate)
• New discount rate: 7.5% (increased)
• Time to maturity: 5 years initially

Analysis:

1. Initial Situation:

   • When the discount rate was 6.5%, the bond traded at a premium ($102.08) because its coupon rate (7%) was higher than the market rate (6.5%).

2. Rate Increase:

   • When the discount rate increases to 7.5% (higher than the coupon rate of 7%), the bond's price immediately drops below par value.
   • At 7.5% discount rate, the bond becomes a discount bond.

3. Price Path to Maturity:

   • For a discount bond (price < par), as it approaches maturity, the price will increase toward the par value of $100.
   • This is known as "pull to par" - the bond's price converges to its par value as maturity approaches.

4. Sequence of Events:

   • First: Price decreases immediately when rates increase from 6.5% to 7.5%
   • Then: Price increases gradually over the remaining life as the bond approaches maturity and its price converges to $100 par value

Why not the other options:

• B (increases then decreases): This would describe a premium bond after a rate decrease
• C (decreases then remains unchanged): Bond prices don't remain unchanged as they approach maturity; they converge to par value

Mathematical Insight: The bond price at 7.5% discount rate can be calculated as: $P = \frac{7}{1.075} + \frac{7}{(1.075)^2} + \frac{7}{(1.075)^3} + \frac{7}{(1.075)^4} + \frac{107}{(1.075)^5}$ This price will be less than $100, and will increase toward $100 as time passes.