Respuesta :
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
