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 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

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