- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 6. The Time Value of Money
- Subject 4. 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**

Consider a level perpetuity of $250.00 with the first payment made at t = 4. The present value of the perpetuity today if the discount rate is 6%, is ______.

A. $3300.39

B. $3498.42

C. $4166.67

**Explanation:**Using Texas Instruments BA II Plus:

Don't forget to clear your calculator's memory, using 2nd QUIT and 2nd CLR WORK.

4166.67 ± FV: FV = - 4,166.67

3 N: N = 3.00

6 I/Y: I/Y = 6.00

CPT PV: PV = 3498.42

(Note: If you work out the future value on your calculator and it is taken to more than 2 decimal places, your final answer may be PV = 3498.41.)

Using Hewlett Packard hp 12 C:

f CLEAR FIN: 0.00000000

f CLEAR REG: 0.00000000

3 n: 3.00000000

6 i: 6.00000000

4166.67 CHS FV: - 4,166.670000

g END: -4,166.670000

PV: 3498.416478

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**User Contributed Comments**
19

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

examcfa |
t=4 is 3N? today is t0 right? |

Eckhardt1978 |
PV(t=3)=A/r --> PV(t=0)=PV(t=3)/(1+r)^3 |

JP09 |
When calculating the present value of a perpetuity you are assuming that the first payment will take place at t1 and the PV is at t0. Since we are getting the 1st payment at t4 the PV of a perpituity PV = Pymnt/r is the PV at t3. Then we have to discount back to t0 by using N=3. Hope that helps! |

tonypractice |
how did the FV $4,166 appear?? |

chamad |
tonypractice : 250/0.06 at T4----perpetuity formula--Than you have to calculate PV at T0 |

tkwangju |
JP09 is right. Thanks |

charlesgallo |
good job team |

Gooner7 |
Thanks JP09 |

soukhov |
beg 4 = end 3 |

Silentdud |
Fantastic problem... I didn't even catch the trick. |

LogicMan |
Thanks guys. I like this site! |

praj24 |
N=3! IT EQUALS 3 ARRRGGGHH |

Ermilova |
I have tried million times..and PV is 3231 on my calc. Don't understand where is a mistake (( |

sarasyed5 |
@ermilova I'm having the same problem... i think we need to reset our calculators or something |

iliavko |
so do we have a "year 0" then??? I don't get the logic of calculating N3 for t=4! |

gyee2012 |
@chamad thanks for pointing out the 250/.06 = 4166.67 |

gyee2012 |
Perpetuity FV = PMT/ i |

megageorge |
i cant get the explanation of n=3, why not 4? |

aprison |
Perpetuity start at T4, so the PV time =3. Calculate the PV of N3 FV250 I/Y = 3 equal to: 209.9048. Perpetuity formula is D/r with D = 209.9048/6% The answer is 3498.42 |