- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 2. Time Value of Money in Finance
- Subject 2. Fixed Income Instruments and the Time Value of Money

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**CFA Practice Question**

A 10-year government zero coupon bond is currently yielding 6.4%. If in 10 years, you expect a two year government zero coupon bond to provide a yield of 10.7%, what must the yield be on a 12-year zero coupon bond today in order for you to be indifferent between the 10-year bond and the 12-year bond?

A. 7.1%

B. 7.7%

C. 8.4%

**Explanation:**To be indifferent, both securities must yield the same total dollar amount at the end of the investment horizon, which, in this case, is 12 years.

Option I: Buy a 10-year bond and then a two-year bond.

Option II: Buy a 12-year bond.

When indifferent: Option I = Option II

(1.064)

^{10}(1.107)

^{2}= (1 + x)

^{12}

= 7.1%

where x is the yield on the 12-year bond.

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**User Contributed Comments**
12

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

rgat |
why isn't the 10 yr and 12 yr forwards not divided by 2?? |

mountaingoat |
anyone help explain the logic behind the calculation: FV(10yr)*FV(2yr) = FV(12yr)? |

ridone |
6.4% is the yield in 10 of 12 years and 10.7% is the yield in 2 of 12 years hence (6.4x10/12)+(10.7x2/12)=7.11% |

jmelville |
rgat - I think you don't need to divide by 2 since it's a zero coupon bond |

JeremyMartin |
i thought we should always assume that coupon rates are semiannual? when should we assume that rates are annual or semiannual? |

YOUCANDOIT |
good question |

danceadam |
The above answer is wrong. You should always use semi annual rates when valuing zero coupon bonds. |

jfrank7 |
The answer is the same if you assume semi-annual payments and divide the interest rates by 2. |

maria15 |
Ridone - I like your take on the calculation. Thanks! |

birdperson |
jfrank7 - i disagree! ((1 + (.064/2))^20 * (1 +(.107/2))^4 ) ^ (1/12) - 1 = 7.237% not 7.1% which you get following the solution provided by analystnotes! |

raywen8 |
^ (1/24) instead of ^ (1/12) |

ascruggs92 |
that was way easier than I thought |