Interest Rate Sensitivity A bond trader purchased each of the following bonds at a yield to maturity of 10%. Immediately after she purchased the bonds, interest rates fell to 6%. What is the percentage change in the price of each bond after the decline in interest rates? Fill in the following table. Round your answers to two decimal places.Price @ 10%Price @ 6%Percentage Change10-year, 10% annual coupon$ $ %10-year zero%5-year zero%30-year zero%$100 perpetuity% Solution Price @ 10% Price @ 6% Percentage Change 10-year, 10% annual coupon 999.94 1294.42 29% 10-year zero 385.5 558.4 45% 5-year zero 620.9 747.3 20% 30-year zero 57.3 174.1 204% $100 perpetuity 1000 1667 67% 10-year, 10% annual coupon - Assuming Face value 1000$ Year Cash flow ( Coupon @ 10%+ Redemption Price ) PVF @ YTM 10% Price of Bond @ 10% YTM PVF @ YTM 6% Price of Bond @ 6% YTM 1 100 0.9091 90.91 0.9434 94.34 2 100 0.8264 82.64 0.89 89 3 100 0.7513 75.13 0.8396 83.96 4 100 0.683 68.3 0.7921 79.21 5 100 0.6209 62.09 0.7473 74.73 6 100 0.5644 56.44 0.705 70.5 7 100 0.5132 51.32 0.6651 66.51 8 100 0.4665 46.65 0.6274 62.74 9 100 0.4241 42.41 0.5919 59.19 10 1100 0.3855 424.05 0.5584 614.24 Price of the Bond 999.94 1294.42 10-year zero - Assuming Face value 1000$ Year Cash flow ( Coupon @ 0%+ Redemption Price ) PVF @ YTM 10% Price of Bond @ 10% YTM PVF @ YTM 6% Price of Bond @ 6% YTM 1 0 0.9091 0 0.9434 0 2 0 0.8264 0 0.89 0 3 0 0.7513 0 0.8396 0 4 0 0.683 0 0.7921 0 5 0 0.6209 0 0.7473 0 6 0 0.5644 0 0.705 0 7 0 0.5132 0 0.6651 0 8 0 0.4665 0 0.6274 0 9 0 0.4241 0 0.5919 0 10 1000 0.3855 385.5 0.5584 558.4 Price of the Bond 385.5 558.4 5-year zero - Assuming Face value 1000$ Year Cash flow ( Coupon @ 0%+ Redemption Price ) PVF @ YTM 10% Price of Bond @ 10% YTM PVF @ YTM 6% Price of Bond @ 6% YTM 1 0 0.9091 0 0.9434 0 2 0 0.8264 0 0.89 0 3 0 0.7513 0 0.8396 0 4 0 0.683 0 0.7921 0 5 1000 0.6209 620.9 0.7473 747.3 Price of the Bond 620.9 747.3 30-year zero - Assuming Face value 1000$ Year Cash flow ( Coupon @ 0%+ Redemption Price ) PVF @ YTM 10% Price of Bond @ 10% YTM PVF @ YTM 6% Price of Bond @ 6% YTM 30th Year 1000 0.0573 57.3 0.1741 174.1 Price of the Bond 57.3 174.1 $100 perpetuity Applying Gordon Model Price of the Bond $100/Ytm @ 10% 1000 $100/ YTM @ 6%. 1667 Price @ 10% Price @ 6% Percentage Change 10-year, 10% annual coupon 999.94 1294.42 29% 10-year zero 385.5 558.4 45% 5-year zero 620.9 747.3 20% 30-year zero 57.3 174.1 204% $100 perpetuity 1000 1667 67% 10-year, 10% annual coupon - Assuming Face value 1000$ Year Cash flow ( Coupon @ 10%+ Redemption Price ) PVF @ YTM 10% Price of Bond @ 10% YTM PVF @ YTM 6% Price of Bond @ 6% YTM 1 100 0.9091 90.91 0.9434 94.34 2 100 0.8264 82.64 0.89 89 3 100 0.7513 75.13 0.8396 83.96 4 100 0.683 68.3 0.7921 79.21 5 100 0.6209 62.09 0.7473 74.73 6 100 0.5644 56.44 0.705 70.5 7 100 0.5132 51.32 0.6651 66.51 8 100 0.4665 46.65 0.6274 62.74 9 100 0.4241 42.41 0.5919 59.19 10 1100 0.3855 424.05 0.5584 614.24 Price of the Bond 999.94 1294.4.

1. Interest Rate Sensitivity
A bond trader purchased each of the following bonds at a yield to maturity of 10%. Immediately
after she purchased the bonds, interest rates fell to 6%. What is the percentage change in the
price of each bond after the decline in interest rates? Fill in the following table. Round your
answers to two decimal places.Price @ 10%Price @ 6%Percentage Change10-year, 10% annual
coupon$ $ %10-year zero%5-year zero%30-year zero%$100 perpetuity%
Solution
Price @ 10%
Price @ 6%
Percentage Change
10-year, 10% annual coupon
999.94
1294.42
29%
10-year zero
385.5
558.4
45%
5-year zero
620.9
747.3
20%
30-year zero
57.3
174.1
204%
$100 perpetuity
1000
1667
67%
10-year, 10% annual coupon - Assuming Face value 1000$
Year
Cash flow ( Coupon @ 10%+ Redemption Price )

2. PVF @ YTM 10%
Price of Bond @ 10% YTM
PVF @ YTM 6%
Price of Bond @ 6% YTM
1
100
0.9091
90.91
0.9434
94.34
2
100
0.8264
82.64
0.89
89
3
100
0.7513
75.13
0.8396
83.96
4
100
0.683
68.3
0.7921
79.21
5
100
0.6209
62.09
0.7473
74.73
6
100

3. 0.5644
56.44
0.705
70.5
7
100
0.5132
51.32
0.6651
66.51
8
100
0.4665
46.65
0.6274
62.74
9
100
0.4241
42.41
0.5919
59.19
10
1100
0.3855
424.05
0.5584
614.24
Price of the Bond
999.94
1294.42
10-year zero - Assuming Face value 1000$
Year
Cash flow ( Coupon @ 0%+ Redemption Price )
PVF @ YTM 10%
Price of Bond @ 10% YTM

4. PVF @ YTM 6%
Price of Bond @ 6% YTM
1
0
0.9091
0
0.9434
0
2
0
0.8264
0
0.89
0
3
0
0.7513
0
0.8396
0
4
0
0.683
0
0.7921
0
5
0
0.6209
0
0.7473
0
6
0
0.5644
0

5. 0.705
0
7
0
0.5132
0
0.6651
0
8
0
0.4665
0
0.6274
0
9
0
0.4241
0
0.5919
0
10
1000
0.3855
385.5
0.5584
558.4
Price of the Bond
385.5
558.4
5-year zero - Assuming Face value 1000$
Year
Cash flow ( Coupon @ 0%+ Redemption Price )
PVF @ YTM 10%
Price of Bond @ 10% YTM
PVF @ YTM 6%
Price of Bond @ 6% YTM

6. 1
0
0.9091
0
0.9434
0
2
0
0.8264
0
0.89
0
3
0
0.7513
0
0.8396
0
4
0
0.683
0
0.7921
0
5
1000
0.6209
620.9
0.7473
747.3
Price of the Bond
620.9
747.3
30-year zero - Assuming Face value 1000$
Year
Cash flow ( Coupon @ 0%+ Redemption Price )

7. PVF @ YTM 10%
Price of Bond @ 10% YTM
PVF @ YTM 6%
Price of Bond @ 6% YTM
30th Year
1000
0.0573
57.3
0.1741
174.1
Price of the Bond
57.3
174.1
$100 perpetuity
Applying Gordon Model
Price of the Bond
$100/Ytm @ 10%
1000
$100/ YTM @ 6%.
1667
Price @ 10%
Price @ 6%
Percentage Change
10-year, 10% annual coupon
999.94
1294.42
29%
10-year zero
385.5
558.4
45%
5-year zero
620.9
747.3
20%
30-year zero

8. 57.3
174.1
204%
$100 perpetuity
1000
1667
67%
10-year, 10% annual coupon - Assuming Face value 1000$
Year
Cash flow ( Coupon @ 10%+ Redemption Price )
PVF @ YTM 10%
Price of Bond @ 10% YTM
PVF @ YTM 6%
Price of Bond @ 6% YTM
1
100
0.9091
90.91
0.9434
94.34
2
100
0.8264
82.64
0.89
89
3
100
0.7513
75.13
0.8396
83.96
4
100
0.683
68.3

9. 0.7921
79.21
5
100
0.6209
62.09
0.7473
74.73
6
100
0.5644
56.44
0.705
70.5
7
100
0.5132
51.32
0.6651
66.51
8
100
0.4665
46.65
0.6274
62.74
9
100
0.4241
42.41
0.5919
59.19
10
1100
0.3855
424.05

10. 0.5584
614.24
Price of the Bond
999.94
1294.42
10-year zero - Assuming Face value 1000$
Year
Cash flow ( Coupon @ 0%+ Redemption Price )
PVF @ YTM 10%
Price of Bond @ 10% YTM
PVF @ YTM 6%
Price of Bond @ 6% YTM
1
0
0.9091
0
0.9434
0
2
0
0.8264
0
0.89
0
3
0
0.7513
0
0.8396
0
4
0
0.683
0
0.7921
0

11. 5
0
0.6209
0
0.7473
0
6
0
0.5644
0
0.705
0
7
0
0.5132
0
0.6651
0
8
0
0.4665
0
0.6274
0
9
0
0.4241
0
0.5919
0
10
1000
0.3855
385.5
0.5584
558.4

12. Price of the Bond
385.5
558.4
5-year zero - Assuming Face value 1000$
Year
Cash flow ( Coupon @ 0%+ Redemption Price )
PVF @ YTM 10%
Price of Bond @ 10% YTM
PVF @ YTM 6%
Price of Bond @ 6% YTM
1
0
0.9091
0
0.9434
0
2
0
0.8264
0
0.89
0
3
0
0.7513
0
0.8396
0
4
0
0.683
0
0.7921
0
5
1000

13. 0.6209
620.9
0.7473
747.3
Price of the Bond
620.9
747.3
30-year zero - Assuming Face value 1000$
Year
Cash flow ( Coupon @ 0%+ Redemption Price )
PVF @ YTM 10%
Price of Bond @ 10% YTM
PVF @ YTM 6%
Price of Bond @ 6% YTM
30th Year
1000
0.0573
57.3
0.1741
174.1
Price of the Bond
57.3
174.1
$100 perpetuity
Applying Gordon Model
Price of the Bond
$100/Ytm @ 10%
1000
$100/ YTM @ 6%.
1667