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A semiannual payment bond with a $1,000 par has a 7 percent quoted coupon rate, a...

A semiannual payment bond with a $1,000 par has a 7 percent quoted coupon rate, a 7 percent promised YTM, and 10 years to maturity. Find the bond's duration.

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Expert Solution

Answer :

Calculation of Bond's Duration :

Below is the table showing calculation of Bond's Duration:

Year (Weights) Cah Flows PVF @3.5% Discounted Cash Flows Weights * Discounted Cash Flows
1 35 0.966183575 33.81642512 33.81642512
2 35 0.9335107 32.67287451 65.34574903
3 35 0.901942706 31.5679947 94.7039841
4 35 0.871442228 30.50047797 122.0019119
5 35 0.841973167 29.46906084 147.3453042
6 35 0.813500644 28.47252255 170.8351353
7 35 0.785990961 27.50968362 192.5677854
8 35 0.759411556 26.57940447 212.6352357
9 35 0.733730972 25.68058403 231.1252562
10 35 0.708918814 24.81215848 248.1215848
11 35 0.684945714 23.97309998 263.7040998
12 35 0.661783298 23.16241544 277.9489853
13 35 0.639404153 22.37914535 290.9288896
14 35 0.61778179 21.62236266 302.7130772
15 35 0.596890619 20.89117165 313.3675748
16 35 0.576705912 20.18470691 322.9553106
17 35 0.557203779 19.50213228 331.5362488
18 35 0.53836114 18.84263988 339.1675179
19 35 0.52015569 18.20544916 345.9035341
20 1035 0.502565884 520.1556904 10403.11381
Total 1000 14709.83742

Coupon Payment in every six month = 1000 * 7%/2 = 35

Years to maturity = 10 * 2 = 20 (Multiplied by 2 as semi annual coupon payment)

Yield to maturity = 7% / 2 = 3.5%

Duration = [Sum of (Weights * Discounted Cash Flows)] / Discounted Cash Flows

= 14,709.83742 / 1000

= 14.70983742 half years or 7.354918709 years or 7.35 years.

jeff jeffy answered 2 years ago
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