- 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)

###
**CFA Practice Question**

Congratulations, you have won the lottery! Your prize is 50 payments of $200,000. The payments will be made at the end of each of the next 50 years. You plan to invest the payments at a rate of 7% per year. What is the present value of your lottery prize?

A. $10,000,000.00

B. $2,953,359.71

C. $2,760,149.26

###
**User Contributed Comments**
9

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

mansi |
can any one please explain how to do it with the calculator? |

flobeebhead |
PMT = $200,000, n = 50, i = 7, FV = 0, solve for PV |

CFAlearner |
I tried that and get $8,412,918.59. What am I doing wrong? |

jalbr270 |
You must divide i by 12. |

Allen88 |
I used the Present Value Annuity formula and got the correct answer. @jalb, i don't think you need to divide by 12. |

BmyOwnBoss |
I entered in the formula as you noted flobeebhead in baII plus however i get 2,675,027.96 instead.. what could be the problemo? |

ksnider |
if you calculate it using the CF function on the calculator you get the correct answer |

dipu617 |
In the BA II Plus, Texas Instrument: PMT= 200,000; I/Y=7; N=50; [CPT] PV= -2,760,149.26 |

kingdave |
this is a present value of annuity because you have a cash flow received which is reinvested each time at the rate 7%, which is the discounting factor you can get the discounting annuity value by doing, ((1+0.07)^50-1)/(0.07*(1+0.07)^50), and then you multiply it by the cash flow in this case which is 200,000 |