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**CFA Practice Question**

Assume that during the past year the consumer price index increased by 3 percent and the securities listed below returned the following real rates of return.

U.S. Long-term bonds: 3.75%

U.S. Government T-bills: 3.50%

U.S. Long-term bonds: 3.75%

What are the nominal rates of return for each of these securities?

A. 6.81%; 8.86%

B. 6.61%; 6.86%

C. 6.61%; 8.86%

**Explanation:**The nominal risk-free rate is defined by the following equation: nominal RFR = [(1 + real RFR) x (1 + expected inflation rate)] - 1.

In this case, nominal RFR for T-bills = [(1 + .035) x (1 + .03)] - 1 = .06605 = 6.61%

and nominal RFR for long-term bonds = [(1 + .0375) x (1 + .03)] - 1 = .068625 = 6.86%.

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**User Contributed Comments**
6

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

NickPash |
What happened to formula Nominal RFR = RFR+E(INF) |

mekc |
either method would lead you to the conclusion of B as 8.86% is way out |

boddunah |
rfr + inf = nominal rfr used in pure expectations theory of yield curve. |

shiva5555 |
It is the only answer that makes sense, the other spreads are too big. |

jdizzle |
rfr + inf = nominal is only an approximation. The real forumula is: (1 + rfr)*(1+inf)=(1+nominal) |

MaresaJaden |
Thanks Jdizzle. In this case approximation works too but I was confused. |