- CFA Exams
- CFA Exam: Level I 2021
- 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**

You wish to accumulate $500,000 by making annual deposits of $9,869.82 into a money market account. All deposits will be made at the beginning of each year. The account pays an interest rate of 16%. How many deposits will be necessary?

B. 14

C. 50

A. 13

B. 14

C. 50

Correct Answer: B

BGN; FV = $500,000; PMT = -$9,869.82; i = 16%; CPT n = 14

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**User Contributed Comments**
18

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

Laurel |
Don't understand how to use the calculation to get this answer. |

tawi |
I got 14 but it does not seem practical |

KD101 |
Tawi Power of compounding and 16% return - Imagine you had fund returning 16%. If you just put $100 at the begining - it would be $799 (no more adding any monthly into it) |

Gina |
if by formula:
500,000 = 9869.82*[((1+.16)^N-1)/.16] * (1+.16) 43.67*(.16)=((1.16)^N - 1 7.99=1.16^N log(7.99)/log(1.16)=14.00 |

geet |
i get 13.99.....so doesn't that mean only 13 payments are required and it accumulates to 500000 by time 13.99 so the 14th payment isnt required..? |

ivot66 |
by the solution you are supposed to get n=14.99!!!! |

ivot66 |
oops my bad the PV value has to be "0" |

cptp |
How can I do it using TI Ba2? |

octavianus |
Don't forget to set your calculator to BEGINNING payments for Annuity DUE |

bobert |
I got 51 the first time I calculated it and I don't know why. When I saw the answer was 14 I redid the problem and it worked. Does anyone have any idea where I went wrong so I do not make the same mistake again? |

StanleyMo |
Hello Bobert: that because you have key 0.16 instead of 16 for the I/Y |

mordja |
useing T1 BA2 set BGN mode set P/Y = 1 FV = 500,000 PMT = -9869.82 I/Y = 16 CPT N result 14.00 |

BMore |
Here's how I did it using the formula: 500000 = 9869.82 * (((1.16^n)-1)/.16) * 1.16 43.6719 = ((1.16^n)-1)/.16 (log 7.9875 / log 1.16) = n n ~ 13.99 or 14 |

johntan1979 |
It's actually 13.99999765, not 13.99 which is very sloppy work by any standards. |

chipster |
TI BAII CALC: 2nd BGN 500,000 FV -9869.2 PMT 16 I/Y CPT-->N = 14 |

msk500 |
Each time I try solving for n, I get this error message. Can anyone tell please tell me why? |

eisenherz |
msk500, you always need to enter opposite signs for PV or PMT and FV - if you try entering minus PV, you will not get error |

mcbreatz |
Can someone explain to me why I am wrong but using the equation where LN(7.99)=LN(1.16)n gives us the n for a regular annuity? Since payments are made at the beginning of the year its actually an annuity due and would require one lass payment? Resulting in the correct answer being 13? |