Period | Years to Maturity | Spot Rate |

1 | .5 | 4.250% |

2 | 1 | 4.750% |

3 | 1.5 | 5.050% |

4 | 2.0 | 7.000% |

5 | 2.5 | 8.750% |

6 | 3.0 | 9.250% |

**A**: 4th period forward rate can be derived from spot rates of 5th period and4th period.
Forward rate = [(1 + 5th_spot_rate / 2)^5 / (1 + 4th_spot_rate / 2)^4] -1 = [(1 + 0.0875/2)5/(1 + 0.0700/2)4] -1 = 7.95%. Annualized the rate one gets 15.9%.
*Bonus Points*

- forward rates assess the future interest rate for some period in the future. Useful when one can't decide how long to hold a bond, such as 4 periods or 5 periods.
- The notation (1)f(4): the subscript before "f" is the length of time that the rate applies (ie. 1 period=6 months). The subscript after "f" refers to the period when the forward rate begins (ie. 4 periods = 2 years into the future).

*Category: C++ Quant > Debt > Valuation*

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