What is the Macaulay duration of a 5.4 percent coupon bond with nine years to ma
ID: 2731950 • Letter: W
Question
What is the Macaulay duration of a 5.4 percent coupon bond with nine years to maturity and a current price of $1,055.40? What is the modified duration? (Do not round intermediate calculations. Round your answers to 3 decimal places.) I WILL ONLY RATE IF THE ANSWER IS CORRECT .SERIOUS TUTOR ONLY.
What is the Macaulay duration of a 5.4 percent coupon bond with nine years to maturity and a current price of $1,055.40? What is the modified duration? (Do not round intermediate calculations. Round your answers to 3 decimal places.) I WILL ONLY RATE IF THE ANSWER IS CORRECT .SERIOUS TUTOR ONLY.
Explanation / Answer
Here first we need to compute Yield to maturity of this bond.
We have:
N = 9
FV=1000
PV= 1055.40
Pmt = 1000 x 5.40% = 54
t
CF
PVF 4.6333%
t x CF x PVF
1
54
0.955718686
51.61
2
54
0.913398207
98.65
3
54
0.872951734
141.42
4
54
0.834296285
180.21
5
54
0.797352549
215.29
6
54
0.76204473
246.90
7
54
0.728300388
275.30
8
54
0.69605029
300.69
9
54
0.665228269
323.30
9
1000
0.665228269
5987.05
7820.42
Macaulay Duration = sum of t x CF x PVF / PV
= 7820.42 / 1055.40
= 7.410
Modified duration = Macaulay duration / ( 1+ R/2)
= 7.41 / ( 1+0.046333/2)
= 7.242
t
CF
PVF 4.6333%
t x CF x PVF
1
54
0.955718686
51.61
2
54
0.913398207
98.65
3
54
0.872951734
141.42
4
54
0.834296285
180.21
5
54
0.797352549
215.29
6
54
0.76204473
246.90
7
54
0.728300388
275.30
8
54
0.69605029
300.69
9
54
0.665228269
323.30
9
1000
0.665228269
5987.05
7820.42
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