Explanation:

This is a bond horizon yield calculation problem. Let's break it down:

Given:

• 30-year bond, 5% annual coupon
• Purchase price: 86.24 (86.24% of par, so $862.40 per $1,000 face value)
• Holding period: 11 years
• Immediately after purchase, interest rates increase by 1%
• Coupons are reinvested at the new yield
• Rates remain at the new level until maturity

Step 1: Calculate the purchase yield At purchase price of 86.24, the yield to maturity (YTM) can be calculated:

• Bond price = 86.24
• Coupon = 5%
• Maturity = 30 years

Using financial calculator or approximation: N = 30, PV = -86.24, PMT = 5, FV = 100 Solve for I/Y ≈ 6.0%

So the original yield was 6.0%.

Step 2: New yield after rate increase Interest rates increase by 1%, so new yield = 6.0% + 1% = 7.0%

Step 3: Calculate bond price after 11 years After 11 years, the bond will have 19 years remaining to maturity (30 - 11 = 19). At 7% yield, the price of a 19-year, 5% coupon bond: N = 19, I/Y = 7, PMT = 5, FV = 100 PV ≈ 79.67

Step 4: Calculate reinvested coupon income Coupons are $5 annually for 11 years, reinvested at 7%. This is a future value of an annuity: PMT = 5, N = 11, I/Y = 7% FV ≈ $78.94

Step 5: Calculate total future value Total future value after 11 years:

1. Sale price of bond: $79.67
2. Reinvested coupons: $78.94 Total FV = $79.67 + $78.94 = $158.61

Step 6: Calculate horizon yield Initial investment: $86.24 Horizon: 11 years Total FV: $158.61

Solve for annual return: PV = -86.24, FV = 158.61, N = 11 I/Y ≈ 6.13%

Verification: The horizon yield of 6.13% is between the original yield (6.0%) and the new yield (7.0%), which makes sense because:

• The investor suffers a capital loss when selling the bond at a lower price (due to higher rates)
• But earns higher reinvestment income on coupons
• The net effect is a realized yield slightly above the original purchase yield

Therefore, the realized horizon yield is closest to 6.13%.