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40. Calculate the modified duration of a 10-year 7% semi-annual coupon bond priced at 97.50. a. 7.316 b....

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Finance

40. Calculate the modified duration of a 10-year 7% semi-annualcoupon bond priced at 97.50.

a. 7.316

b. 7.06

c. 6.88

d. 3.53

e. 3.67

Answer & Explanation Solved by verified expert
4.3 Ratings (855 Votes)

Period Cash flow Period x Cash flow PV of $1 at 3.6788% Present value of cash flow First we have to calculate bonds yield
1 3.5 3.5             0.9645            3.38 PV 97.5
2 3.5 7             0.9303            6.51 FV 100
3 3.5 10.5             0.8973            9.42 PMT 3.5 (100 x 7%/2)
4 3.5 14             0.8654          12.12 NPER 20 (10 x 2)
5 3.5 17.5             0.8347          14.61 Rate(yield) 3.6788% per semi annual period
6 3.5 21             0.8051          16.91 =RATE(20,3.5,-97.5,100)
7 3.5 24.5             0.7766          19.03
8 3.5 28             0.7490          20.97
9 3.5 31.5             0.7224          22.76
10 3.5 35             0.6968          24.39
11 3.5 38.5             0.6721          25.87
12 3.5 42             0.6482          27.23
13 3.5 45.5             0.6252          28.45
14 3.5 49             0.6030          29.55
15 3.5 52.5             0.5816          30.54
16 3.5 56             0.5610          31.42
17 3.5 59.5             0.5411          32.19
18 3.5 63             0.5219          32.88
19 3.5 66.5             0.5034          33.47
20 103.5 2070             0.4855    1,005.01
Total    1,426.69
÷ 97.5
Maculay Duration     14.6327 period
Modified duration = Maculay duration / (1+yield)
=14.6327/1.036788
14.11349 semi annual periods
Or (14.11349/2)            7.06 Annual Option B is right

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Transcribed Image Text

40. Calculate the modified duration of a 10-year 7% semi-annualcoupon bond priced at 97.50.a. 7.316b. 7.06c. 6.88d. 3.53e. 3.67

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