Question

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Find the duration of a bond with settlement date June 14, 2016, and maturity date December...

Find the duration of a bond with settlement date June 14, 2016, and maturity date December 21, 2025. The coupon rate of the bond is 8%, and the bond pays coupons semiannually. The bond is selling at a yield to maturity of 9%. (Do not round intermediate calculations. Round your answers to 4 decimal places.)

Macaulay duration
Modified duration

Solutions

Expert Solution

Number of Periods = 9.5* 2= 19
Coupon semiannual = 8%*1000 /2 = 40
Rate = 9%/2= 4.5

Time(n) Cash flow PV of Cash flow=(Cash flow)/(1+4.5%)^n PV*Time
1 40 38.28 38.277512
2 40 36.63 73.2583961
3 40 35.05 105.155592
4 40 33.54 134.169815
5 40 32.10 160.490209
6 40 30.72 184.294977
7 40 29.39 205.751968
8 40 28.13 225.019241
9 40 26.92 242.245594
10 40 25.76 257.571073
11 40 24.65 271.127445
12 40 23.59 283.038655
13 40 22.57 293.421253
14 40 21.60 302.384803
15 40 20.67 310.032265
16 40 19.78 316.460367
17 40 18.93 321.759942
18 40 18.11 326.016266
19 1040 450.63 8562.04334
Total 937.0335 12612.5187
Maculay Duration 13.4601 (=12612.5187/937.0335)
Modified Duration 12.8804 (=Maculay Duration/(1+YTM)

So Maculay Duration in terms of years = 13.4601/2 = 6.7300
Modified duration = 12.8804/2 = 6.4402

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