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Bond A has a 7% coupon rate, paid annually. Maturity is in three years. The bond...

Bond A has a 7% coupon rate, paid annually. Maturity is in three years. The bond sells at par value $1000. The modified diration of this bond is ____ and the dollar duration of this bond is ____.

A. 2.81, 2810
B. 2.59, 2590
C. 2.65, 2650
D. 2.62, 2620
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Homework Answers

Answer #1

Step-1, Calculation of Macaulay Duration of the Bond

Years (1)

Annual cash flow (2)

Present Value Factor at 7.00% (3)

Present Value of the cash flows

(4) = (3) x (2)

Weight to total value

(5)

Duration

(6) = (1) x (5)

1

70.00

0.93458

65.42

0.06542

0.0654

2

70.00

0.87344

61.14

0.06114

0.1223

3

1,070.00

0.81630

873.44

0.87344

2.6203

TOTAL

$1,000

2.8080 Years

Macaulay Duration = 2.8080 Years

Step-2, Calculation of Modified Duration of the Bond

Modified Duration of the Bond = Macaulay Duration / (1 + YTM)

= 2.8080 Years / (1 + 0.07)

= 2.8080 Years / 1.07

= 2.62 Years

The dollar duration of this bond = 2.62 Years x 1,000 = 2,620

Therefore,

The Modified duration of this bond is 2.62 Years

The Dollar duration of this bond is 2,620

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