- CFA Exams
- CFA Level I Exam
- Topic 6. Fixed Income
- Learning Module 44. Introduction to Fixed-Income Valuation
- Subject 7. The Maturity Structure of Interest Rates

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**CFA Practice Question**

If you can invest for two years at 5% today, or invest for 1.5 years at 4.6%, what would you have to earn on your reinvestment to be just as well off?

A. 3.102%

B. 5.40%

C. 6.204%

**Explanation:**(1+.05/2)

^{4}/ (1+.046/2)

^{3}-1 = .03102

Annual = 3.102 x 2 = 6.204

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**User Contributed Comments**
9

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

ehc0791 |
"semi-annual" compounding should be assumed if not specified. |

uberstyle |
don't forget to double your answer to get to annualized rate. I made a stupid mistake here... |

micheleus |
could anyone explain more? |

Criticull |
logical you could say that the reinvestment rate has to be larger than 5.4, since you would only being achieving that for a quarter of the total time period, which on a weighted average basis could not make up for the foregone .4% over the first 3 6-months periods. Better to know how to do it though. |

zzhumanov |
firstly:I bond, N=2; Pv=100, I=5% => FV=110.25 II bond, N=1.5; Pv=100,i=4.6% => FV=106.98 then: Pv=106.98; Fv=110.25, N=0.5 => i=6.206 |

kellyyang |
ZZhumanov your provide answer has a little sightly wrong: N=2, FV=100, I=5% ->PV=90.70 N=1.5, FV=100, I=4.6%->PV=93.47 -pv=90.70, FV=93.47 N=.5 ->i=6.20 |

yekky |
What formula is this or what concept is it using? I solved it correctly knowing that your reinvestment rate should be HIGHER than your given yields if you want to make money. Could someone shed some light on this question? |

jayj001 |
5*(1.05^2) = 5.5125 5*(1.046^1.5) = 5.3489 5.3489* (1+x)^0.5 = 5.5125 x = 6.21% |

dash1s |
yekky, the formula is: (1+S4)^4=(1+S3)^3*(1+1F3) |