- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 1. The Time Value of Money
- Subject 2. The Future Value and Present Value of a Series of Equal Cash Flows (Ordinary Annuities, Annuity Dues, and Perpetuities)

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**CFA Practice Question**

You are to receive $1500 every year forever from the federal government as the winner of the national fiscal prudency and awareness contest. The government has also provided you with the option of choosing $1700 per year over the next 30 years. Payments are to be received semi-annually. If the market rate of interest is 8% annually, what is the value of the two options?

B. $18,750; $19,230

C. $18,750; $19,138

A. $18,382; $10,323

B. $18,750; $19,230

C. $18,750; $19,138

Correct Answer: B

(1500/2)/0.04 = 18,750; N=60, I=4%, PMT=850,FV=0, PV=? = 19,229.97

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**User Contributed Comments**
18

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

lna1717 |
8% is stated annual interest rate thus should be divided by 2. EAR = (1+8%/2)^(30*2) |

eaglei |
wrong Ina1717. EAR = (1+.05/2)^2 NOT ^(30*2) |

eaglei |
oops. i mean EAR = (1+.08/2)^2 |

mtcfa |
Here's an easier way:set periods/year to 2, then i = 8%, pmt = 850, n = 60. You don't have to mess with the EAR stuff. |

shanerbaner |
its good to know though |

cntosg |
Just take the semi-annual interest rate and take N=60, can already... |

lexi |
Where does the .4 come from? |

nike |
semi-annual interest rate of 8% is 4% - 0.04. |

Ioannis |
To find the effective rate in semiannual terms of an annual 8% do: (1+EFF)^(N*2)=(1+8%)^N Set N=1 or take Nth roots =>(1+EFF)^2=(1+8%)=> =>1+EFF^2+2EFF=1+8%=> EFF^2<<1 hence ignore =>1+2EFF=1+8%=> =>EFF=8%/2=4% |

Ioannis |
For monthly divide by 12 to get EFF=NOM/12 For quarterly divide by 4 to get EFF=NOM/4 |

HeroEarth |
where does the N=60 come from? |

hoyleng |
HeroEarth : N = 60 is because "payment are to be received semi-annually". Thus 30yrs X 2 = 60 payments |

MXMX |
I think of using EAR. After computing EAR = (1+0.8/2)^2 - 1 = 8.16% Then make a calculation for PV like: I/Y = 8.16% N = 30 PMT = 1700 CPT PV = 18,852.908 It should be something wrong with it, right? Anyone plz help? |

johntan1979 |
And that's how the government trick people (as well as those who still can't get the right answer at this point - question #21) into thinking $1,500 annually forever is better. |

gill15 |
I dont get this. Im an actuary and this makes little sense or I've forgotten my basics. If they give you the annual rate we need to try to convert it to a semi annual rate. You cant just divide by 2. (1 + .08) = (1 + Eff)^2. Eff = 3.92% which should be used. If the question said, 8% compounded semi-anually then yes you would divide by 2 for 4% BUT this question gives you the annual rate of 8%. Am I missing something. |

assiduous |
@gill15 I see your logic, however the question states that "payments will be received semi-annually." We are concerned with the PV of an annuity, not EAR. If we are quoted a certain amt to be paid annually but our payments come in the form of semi-annual payments then we must take the annual quote and divided by 2. And since rate per period must match payment per period, we must also divide the quoted annual rate by 2. |

abs013 |
Just solve for the 2nd option it would be a lot faster |

ibrahim18 |
The question assumes compounding semi annually |