A government bond currently carries a yield to maturity of 6 percent and a market price of $1,168.49. If the bond promis...
A government bond currently carries a yield to maturity of 6 percent and a market price of $1,168.49. If the bond promises to pay $100 in interest annually for five years, what is its current duration?
Homework Answers
| Duration of bond = Sum of (present value of cash flow*n)/Price of bond | |||||
| n is the year in which cash flow is received | |||||
| Assuming face value of bond is $1,000 | |||||
| Year (n) | Cash flow | Discount factor @ 6% | Present value | PV*n | |
| 1 | $100.00 | 0.943396226 | $94.34 | $94.34 | 94.34*1 |
| 2 | $100.00 | 0.88999644 | $89.00 | $178.00 | 89*2 |
| 3 | $100.00 | 0.839619283 | $83.96 | $251.89 | 83.96*3 |
| 4 | $100.00 | 0.792093663 | $79.21 | $316.84 | 79.21*4 |
| 5 | $1,100.00 | 0.747258173 | $821.98 | $4,109.92 | 821.98*5 |
| $1,168.49 | $4,950.98 | ||||
| Duration of bond | 4950.98/1168.49 | ||||
| Duration of bond | 4.24 | ||||
| Thus, duration of bond is 4.24 years. | |||||
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