(I) The solution is
Bond Payouts | Time, t | Y(t) | 1+Y(t) | Discount Factor | Present Value |
(1) = Coupon Rate * Bond Price + Bond Price (at t=2) | (2) |
(3) = 0.035-0.015*EXP(-0.5*(2)) |
(4) = 1+(3) | (5) = 1/(4) | (6) = (1) * (5) |
0 | 0 | 0.02 | 1.020 | 0.980392157 | 0.00 |
125 | 0.5 | 0.02 | 1.023 | 0.977213351 | 122.15 |
125 | 1 | 0.03 | 1.026 | 0.974751936 | 121.84 |
125 | 1.5 | 0.03 | 1.028 | 0.972843557 | 121.61 |
2625 | 2 | 0.03 | 1.029 | 0.971362478 | 2549.83 |
SUM | 2915.43 |
Therefore, the purchase price is 2915.43
(II)
Time, t | Present Value | Weighted Present Value |
(1) | (2) (from table above) | (3) = (1) * (2) |
0 | 0.00 | 0.00 |
0.5 | 122.15 | 61.08 |
1 | 121.84 | 121.84 |
1.5 | 121.61 | 182.41 |
2 | 2549.83 | 5099.65 |
SUM | 2915.43 | 5464.98 |
Duration = Weighted Price Value / Current Market Value = 5464.98/2915.43 = 1.875
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