could you please give the right answer and explanation of this problems? Assume
ID: 2728810 • Letter: C
Question
could you please give the right answer and explanation of this problems?
Assume a bond with a $1,000 par value and an 11 percent coupon rate, two years remaining to maturity, and a 10 percent yield to maturity. The modified duration of this bond is
a. 1.73 years.
b. 1.71 years.
c. 1.90 years.
d. none of the above
Assume a bond with a $1,000 par value and an 11 percent coupon rate, two years remaining to maturity, and a 10 percent yield to maturity. The duration of this bond is
a. 1.90 years.
b. 1.50 years.
c. 1.92 years.
d. none of the above
Explanation / Answer
Question 1
We have
FV= 1000
N = 2
Pmt = 1000 x 11% = 110
R= 10%
We can use following formula to compute Macaulay duration:
Macaulay Duration = sum of PV x t / Sum of PV
t
CF
PV factor 10%
PV
PV x t
1
110
0.909090909
100.00
100.00
2
110
0.826446281
90.91
181.82
2
1000
0.826446281
826.45
1652.89
1017.36
1934.71
Dmac = 1934.71 / 1017.36
= 1.901706
Modified duration = Dmac / (1+ R/n)
= 1.901706 / (1+0.10/ 2)
= 1.81
Therefore, none of the above ( option d) is correct.
t
CF
PV factor 10%
PV
PV x t
1
110
0.909090909
100.00
100.00
2
110
0.826446281
90.91
181.82
2
1000
0.826446281
826.45
1652.89
1017.36
1934.71
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