Explanation

To solve this problem, we need to calculate the bond's value before and after the yield change, then find the difference.

Step 1: Initial purchase price and yield calculation

• Bond purchased at $98 (price below par)
• 3-year bond, semiannual payments
• Par value: $100
• Coupon rate: 5% annual → semiannual coupon = $100 × 5% ÷ 2 = $2.50
• Number of periods at purchase: 3 years × 2 = 6 periods

We need to find the initial YTM (yield to maturity) when purchased at $98.

Using the bond pricing formula: $98 = $2.50 × [1 - (1 + r)^(-6)]/r + $100 × (1 + r)^(-6)

Solving for r (semiannual yield): At r = 2.75% (5.5% annual): PV = $2.50 × 5.463 + $100 × 0.852 = $13.66 + $85.20 = $98.86 (too high) At r = 2.80% (5.6% annual): PV = $2.50 × 5.417 + $100 × 0.845 = $13.54 + $84.50 = $98.04 (close) At r = 2.81% (5.62% annual): PV = $2.50 × 5.410 + $100 × 0.843 = $13.53 + $84.30 = $97.83

So initial YTM ≈ 5.6% annual (2.8% semiannual)

Step 2: One year later (after 2 coupon payments)

• Time remaining: 2 years (4 periods)
• YTM decreases by 100 bps (1%) → new YTM = 5.6% - 1% = 4.6% annual
• New semiannual yield = 4.6% ÷ 2 = 2.3%

Step 3: Calculate new bond price New price = $2.50 × [1 - (1.023)^(-4)]/0.023 + $100 × (1.023)^(-4) = $2.50 × [1 - 0.913]/0.023 + $100 × 0.913 = $2.50 × [0.087/0.023] + $91.30 = $2.50 × 3.783 + $91.30 = $9.46 + $91.30 = $100.76

Step 4: Calculate price change Price change = $100.76 - $98 = $2.76

This is closest to option B: $2.73

Key points:

1. When yields decrease, bond prices increase
2. The bond was purchased at a discount ($98), so as it approaches maturity, its price naturally moves toward par
3. The 100 bps yield decrease causes additional price appreciation
4. The slight difference from $2.73 is due to rounding in the YTM calculation

Alternative calculation method: Using financial calculator:

• Initial: N=6, PV=-98, PMT=2.5, FV=100 → I/Y=2.8% (5.6% annual)
• After 1 year: N=4, I/Y=2.3% (4.6% annual), PMT=2.5, FV=100 → PV=100.76
• Change: 100.76 - 98 = 2.76 ≈ $2.73