- 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**

A beginning amount of $75,000 is invested at 13% per year. At the beginning of each year for the next 30 years, a withdrawal is to be made, to pay insurance premiums. What is the largest premium this investment will support?

A. $10,005.80

B. $8,854.69

C. $7,836.01

**Explanation:**BGN, PV = -$75,000; n = 30; i = 13%; CPT PMT = $8,854.69

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**User Contributed Comments**
11

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

LRS24 |
Is this the correct answer, I may be reading it wrong but $75k earns $9750 per year meaning $8,854.69 will easily be provided for without impacting the principle |

Eckhardt1978 |
at lrs24: -75k makes 10,004.4345, the largest premium is 8,854,69 because of 10,005.80 is impossible without impacting the principle. |

chenchow |
I am not sure whether I did it wrong, but I typed PV = -75K, n=30, i=13% into my calculator, and compute PMT, I get $10,005.80 . Anyone in the same shoe? |

vstolin |
Read again: BEGINNING of the year. Switch your calculators to "BEG" and you'll get 88854 |

george2006 |
Watch out for "Begining"... and set BGN on your calculator! |

dg18sox |
not sure why but I pressed Beginning of the year PV =-75k, n=30, i=13 and compute pmt and I get $8,419.70 anyone else have that problem? |

bwbarksdale |
perhaps you still had something loaded in as FV from doing a previous problem. |

aakash1108 |
The basic formula for Annuity is: PV = A[1- (1/(1+ r)^N)/r] Take PV = 75000-A (as 1st Annuity is already paid and cannot be discounted. N = 29 (because the first annuity is already paid, remaining annuities = 29) R = 0.13 With this we get: (75000-A)=A[ 1 - (1/(1.13)^29/0.13)] 0.13(75000-A)=A[1-(1/34.615838)] (Moved 0.13 to the left hand side and simplified (1.13)^29) 9,750 - 0.13A = A (1 - 0.02889) 9,750 - 0.13A = 0.97111A 9,750 = 0.97111A + 0.13A 9,750 = 1.10111A A = 9,750/1.10111 A = 8854.70 |

malikhwa |
On BAII PLUS Clear Previous Work: (2ND)(CLR WORK) Set to Beginning: (2ND)(BGN) (2ND)(SET) 75000(PV) 30(N) 13(I/Y) (CPT)(PMT) |

thekobe |
just be sure to read the instructions, as the problem indicates you have to set the TI to 2nd set and then BGN mode! |

davcer |
just remember to reduce tne periods to n-1 while doing your calculations and finally adding one annuity to your previous answer when the question says begining of the year. |