A 10-year bond has an annual coupon of 8% and face value $1,000. If the yield to maturity is 6%, what is the approximate price of the bond?

A 10-year bond has an annual coupon of 8% and face value $1,000. If the yield to maturity is 6%, what is the approximate price of the bond?

• A. Approximately 1,147
• B. Approximately 980
• C. Approximately 1,030
• D. Approximately 1,200

Answer: (A)

When a bond’s coupon rate exceeds the yield to maturity, the price trades above its face value because investors receive higher periodic income than they would at the going yield. The price equals the present value of all future coupons plus the present value of the face value. Compute: - PV of coupons: 80 × [1 − (1.06)^(−10)] / 0.06 ≈ 80 × 7.360 ≈ 588.8 - PV of principal: 1000 / (1.06)^(10) ≈ 558.4 Total approximate price ≈ 588.8 + 558.4 ≈ 1,147. So the bond would be priced at about 1,147.

When a bond’s coupon rate exceeds the yield to maturity, the price trades above its face value because investors receive higher periodic income than they would at the going yield. The price equals the present value of all future coupons plus the present value of the face value.

Compute:

• PV of coupons: 80 × [1 − (1.06)^(−10)] / 0.06 ≈ 80 × 7.360 ≈ 588.8

• PV of principal: 1000 / (1.06)^(10) ≈ 558.4

Total approximate price ≈ 588.8 + 558.4 ≈ 1,147.

So the bond would be priced at about 1,147.