Question

Find the duration of a 6% coupon bond making annual coupon payments if it has three years until maturity and a yield to maturity of 6%. What is the duration if the yield to maturity is 10%?

Answer 1

Answer and Explanation:

The computation of the duration of the bond is as follows:

For 6% yield to maturity

Year Payment Discount factor at 6% Weight Weight × Year

(Rate × Par value)

a b (a ÷ b)

1 $60 (1.06)^1 = 1.06 $56.60 0.0566 0.0566

(0.06 × $1,000)

2 $60 (1.06)^2 = 1.1236 $53.40 0.0534 0.1068

3 $1,060 (1.06)^3 = 1.1910 $890.00 0.8900 2.6700

($1,000 + $0.06 × $1,000)

Total $1,000 2.8334

hence, the duration of the bond is 2.8334 years

For 10% yield to maturity

Year Payment Discount factor at 10% Weight Weight × Year

(Rate × Par value)

a b (a ÷ b)

1 $60 (1.06)^1 = 1.1 $54.55 0.0606 0.0606

(0.06 × $1,000)

2 $60 (1.06)^2 = 1.21 $49.59 0.0551 0.1101

3 $1,060 (1.06)^3 = 1.3310 $796.39 0.8844 2.6531

($1,000 + $0.06 × $1,000)

Total $900.53 2.8238

hence, the duration of the bond is 2.8334 years