Question

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

a. 7.316

b. 7.06

c. 6.88

d. 3.53

e. 3.67

Answer 1

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