- CFA Exams
- CFA Level I Exam
- Study Session 14. Fixed Income (1)
- Reading 44. Introduction to Fixed-Income Valuation
- Subject 7. The Maturity Structure of Interest Rates

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**CFA Practice Question**

An analyst gathers the following information:

1 5.00%

2 6.00%

3 6.50%

Years to Maturity Spot Rate

1 5.00%

2 6.00%

3 6.50%

Based on the data above and assuming annual compounding, the one-year implied forward rate two years from now is closest to ______.

A. 6.25%

B. 7.01%

C. 7.51%

**Explanation:**[(1 + 6.5%)

^{3}/(1 + 6%)

^{2}]

^{1}- 1 = 7.51%.

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**User Contributed Comments**
10

User |
Comment |
---|---|

synner |
note: [(1.0325^3/1.03^2] -1) *2 = .075 {(1.0325^6/1.03^4)^.5 - 1} * 2 = .075 |

yizhang |
1.065^3/1.06^2-1=7.51% |

Becker |
Can somebody explain ? |

steved333 |
(1+ 3rd-period spot^3)/(1+ 2nd period spot^2)- 1 Third period because it's 1 year after the second year and the question asks for the 1-year rate in the second year... |

dlukas |
A CF occuring in two years would be discounted by dividing by (1.06)^2. A CF occurring in three years would be divided by (1.065)^3. So to discount a CF occurring in 3 years back one year (which is the one-year forward rate two years from now), take (1.065)^3 divided by (1.06)^2--that's your divisor for that CF. Subtract 1 and that's your forward rate. It helps me to take a hypothetical CF and map it out on a timeline to make sure I have all my exponents right. |

otterom |
Thanks, dlukas! |

zed888 |
why don't we assume semi annual compounding? |

bidisha |
Is there a way to do it on baii using the cf function |

miropower |
one can also use approximation: we could approximate as (3x6.50)-(2x6) = 7.50 for a quick answer which is pretty close to 7.51 |

Logaritmus |
May be it easier to get from discount factors (value of 1 at time T), Discount factor function is the best method to describe structure of interest rates. DF(2Y) = 1.06^(-2) = 0.89 DF(3Y) = 1.065^(-3) = 0.82785 Then DF (2Y) * (1+implied rate)^(-1)= DF(3Y) and finally 1 + implied rate = DF(2Y)/DF(3Y) = 1.07507 |