- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 2. Time Value of Money in Finance
- Subject 2. Fixed Income Instruments and the Time Value of Money

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**CFA Practice Question**

An investor aged 24 wishes to accumulate a large amount of money by her 50th birthday. She will pay equal annual payments of $1200 into an account that pays interest at 10 % per annum compounded annually. Payments start on her twenty-fifth birthday and end on her fiftieth birthday. How much will she have accumulated by her 50th birthday?

A. $118,016.47

B. $120,467.28

C. $131,018.12

**Explanation:**Using hp-12C:

f CLEAR FIN: 0.00000000

f CLEAR REG: 0.00000000

26 n: 26.00000000

10 i: 10.00000000

1200 CHS PMT: -1,200.000000

g END: -1,200.000000

FV: 131,018.12

Using TI BA II Plus:

2nd QUIT: 0.00

2nd CLR TVM: 0.00

1200 ± PMT: PMT = - 1,200.00

26 N: N = 26.00

10 I/Y: I/Y = 10.00

CPT FV: 131,018.12

Thus, the series of cash flows of $1000 per year will be worth $131,018.12.

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**User Contributed Comments**
22

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

smithma1 |
This is calculating the FV of an ANNUITY DUE. You put your Texas calc in BGN mode because the first payment is today on her 25th birthday. The answer is then $144,120. The answer suggested as being $131,018 assumes the first payment is in one year's time (ie, that the investor is 24 and in her 25th year of life, that is she's not actually 25 yet). |

danlan |
Question is not clear: end on fiftieth birthday, including fiftieth birthday or not? Also, calculator should be in BGN mode as stated by smithma1 |

Carol1 |
it can also calculated as 25 years regular annual FV plus $1200, which is the last payment at 50 birthday, thus the FV is $119,216.47, any one help me check the answer? |

dimos |
The pmt starts on her 25th birthday so it is ordinary due. You calculate for 25 years and find 129,818.12 but there is one more pmt on her 50th birthday, so just add 1200 and find answer C. |

danlan |
Set N=25, I=10, PV=-1200, PMT=-1200 and we get FV=131018.2 |

volkovv |
danlan that is wrong, those settings won't produced a desired outcome dimos is correct, but you can also calculate it as an ordinary annuity with 26 years: N=26, I=10, PMT=-1,200, CPT FV=131,018 |

Shelton |
1200S(angle 26)10%=-131018.1185 |

Lucho |
The investor is 24, The q suggest at any time she will deposit it first CF, therefore the PMT are 26.. |

labsbamb |
can someone explain if we have to put calculator in begin mode. |

bansal |
PV of 25 payments at the beg of every month + 1200 |

Riyadi |
i dont agree.. i think N should be 26 and mode set to Beg |

georgedai |
I think you should use annuity due because the money starts to be collected on the 25th birthday. N should be 25, because it is on the 50th birthday, which means the end of age 49! The correct answer should be 129,818.12. |

TammTamm |
This makes me upset, I knew I had the right answer but I forgot about the BEG mode. |

AnnieBen |
Payments are made starting on her 25th birthday and ends on her 50th Birthday, which means a payment is made on her 50th birthday. Therefore 26 actual payments are made and you do not us begin mode to get the answer. MMc |

bvides |
Draw a timeline .....wow actually 26..makes sense |

Archer24m |
BEG mode and n=26 is correct. |

bluejazzy1 |
n=26 because inclusive. try 25 to 30 yrs old, its 6 payments. |

endurance |
Agree with AnnieBen - no BGN mode here. The first payment is just covering the first payment. Each payment is covering the latest year which means END mode. The question is very clear about number of payments -> N=26, i=10% PMT=-1200 equals 131,018.12 on her 50th birthday |

RAustin |
Payments start on her 25th bday. End mode (ordinary ann.), then follow rest of instructions. You can also follow dimos' instructions. |

schweitzdm |
Is N=26 assuming she just turned 24 today? |

CFAToad |
There are 26 payments. And the last payment does not receive interest. That is why ordinary annuity and n=26 makes sense. This can also be achieved by incorrectly using an annuity due (which implies that all payments will have at least one period of interest applied) and adding on payment on top. |

edrei7 |
Count payment at 25 years old to 50 years old equating to 26 payments. This is not BEG mode since the investor is still 24. You still have to consider the gap of time value from age 24 to age 25. |