Explanation

To calculate the value of the bond, we need to discount all future cash flows (coupon payments and principal repayment) at the market discount rate of 6%.

Given:

• Coupon rate = 7%
• Par value = $1,000
• Annual coupon payment = 7% × $1,000 = $70
• Market discount rate = 6%
• Time to maturity = 3 years
• Payments are annual

Calculation:

The bond value is the present value of all future cash flows:

1. Year 1 coupon payment: $70 ÷ (1.06)¹ = $70 ÷ 1.06 = $66.0377
2. Year 2 coupon payment: $70 ÷ (1.06)² = $70 ÷ 1.1236 = $62.2997
3. Year 3 coupon payment: $70 ÷ (1.06)³ = $70 ÷ 1.191016 = $58.7733
4. Year 3 principal repayment: $1,000 ÷ (1.06)³ = $1,000 ÷ 1.191016 = $839.6193

Total present value: $66.0377 + $62.2997 + $58.7733 + $839.6193 = $1,026.73

Alternative calculation using formula: Bond Value = C × [1 - (1+r)⁻ⁿ]/r + FV/(1+r)ⁿ Where: C = $70 r = 0.06 n = 3 FV = $1,000

Bond Value = $70 × [1 - (1.06)⁻³]/0.06 + $1,000/(1.06)³ = $70 × [1 - 0.839619]/0.06 + $839.6193 = $70 × [0.160381]/0.06 + $839.6193 = $70 × 2.673017 + $839.6193 = $187.1112 + $839.6193 = $1,026.73

Why this makes sense: When the coupon rate (7%) is higher than the market discount rate (6%), the bond should trade at a premium to its par value. $1,026.73 represents a premium bond, which is consistent with this relationship.

Why other options are incorrect:

• A. $973.76: This would be the value if the coupon rate were lower than the market rate (bond trading at a discount)
• C. $1,049.17: This is too high and doesn't match the correct present value calculation