Detailed Explanation

To calculate the current value (price) of the bond, we need to discount all future cash flows at the yield to maturity (YTM) of 3%.

Bond Details:

• Face value: £1,000
• Coupon rate: 4% (annual)
• Annual coupon payment: £1,000 × 4% = £40
• Maturity: 3 years
• YTM: 3%

Cash Flows:

• Year 1: £40 coupon payment
• Year 2: £40 coupon payment
• Year 3: £40 coupon payment + £1,000 principal repayment = £1,040

Present Value Calculation:

1. Year 1 coupon: £40 ÷ (1.03)¹ = £40 ÷ 1.03 = £38.83
2. Year 2 coupon: £40 ÷ (1.03)² = £40 ÷ 1.0609 = £37.70
3. Year 3 cash flow: £1,040 ÷ (1.03)³ = £1,040 ÷ 1.092727 = £951.70

Total Present Value: £38.83 + £37.70 + £951.70 = £1,028.23

Why the bond trades at a premium:

• The coupon rate (4%) is higher than the YTM (3%)
• Investors are willing to pay more than face value for a bond that pays higher coupons than the current market rate
• The bond's price (£1,028) is above its par value (£1,000)

Verification using bond pricing formula: $P = \frac{C}{(1+r)^1} + \frac{C}{(1+r)^2} + \frac{C+FV}{(1+r)^3}$ $P = \frac{40}{1.03} + \frac{40}{1.03^2} + \frac{40+1000}{1.03^3}$ $P = 38.83 + 37.70 + 951.70 = 1,028.23$

Therefore, the current value of the bond is closest to £1,028 (Option B).