Answer: decreases then increases.

## 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.

Author: LeetQuiz .