- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 1. The Time Value of Money
- Subject 3. The Future Value and Present Value of a Series of Uneven Cash Flows

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**CFA Practice Question**

An individual deposits $1,000 today, $1,200 one year from today, and $1,500 two years from today into an interest-earning account. The deposits earn 10% compounded annually. Find the total accumulated amount in his account three years from today.

Correct Answer: $4,433.00

This is not an annuity, since the cash flows change every year. This uneven cash flow is a stream of annual single cash flows. Find the future value of each cash flow and then add them up. Notice that the payments are made at the beginning of each year. Notice that PMT1 earns interest for 3 years, PMT2 earns interest for 2 years, and PMT3 earns interest for 1 year.

We need to calculate the future value of the 3 investments separately and then add them together. We use the future value formula FVN = PV (1 + r)

^{N}1,000 (1.1)

^{3}+ 1,200 (1.1)^{2}+ 1,500 (1.1)^{1}= 1,331 + 1,452 + 1,650 = 4,433.00This is probably the best method to use, since the NPV functions will only give present value, not future value.

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**User Contributed Comments**
15

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

danlan |
We get NPV=3027.8, the the future value=NPV*1.1^4=4433 |

chuong |
Try it again Co=1000, C1=1200, C2=1500, I=10 =>NPV=3330.57581 then PV=-33057581, I/Y=10, N=3 => FV = 4433 |

Rotigga |
Great tip, chuong! |

julescruis |
nice one |

thekapila |
well here is the correct way to do it. C0 = -1000 C1 = -1200 C2 -1500 I - 10 CMPT NFV - 4433 |

StanleyMo |
This questions is tricky: you have in fact t=0, t=1, and t=2 bank in but they want you to calculate the total amount at t =3 instead of t=2. thats why we are using C1, C2 and C3 with the C1 = 1100 ( not 1000!, that is t=0) |

TammTamm |
Thanks for the two step process chuong. Makes sense now. |

SANTOSHPRABHU |
Using BA II Plus: 2nd reset enter 2nd QUIT: 0.00 CF: CFo = previous value 2nd CLR WORK: CFo = 0.00 1000 ENTER: CFo = 1,000.00 DownArrow: C01 = 0.00 1200 ENTER: C01 = 1,200.00 DownArrow: F01 = 1.00 DownArrow: C02 = 0.00 1500 ENTER: C02 = 1500.00 DownArrow: F02 = 1.00 NPV: I = 0.00 10 ENTER: I = 10.00 DownArrow: NPV = 0.00 CPT: NPV = 3330.58 Thus PV = -3,330.58 N=3 I/Y=10 CPT > FV = 4433.00 |

VT2010 |
can someone solve this one with hp12c please regards vishal |

ThanhBUI |
short cut possible only if identical rates |

johntan1979 |
Throw away your HP12C |

chipster |
got the same thing danlan. |

jonan615 |
HP12C: 1000 [g][cf0] 1200 [g][cfj] 1500 [g][cfj] 10 [i][f][npv] [enter][enter] 1.10 [enter] 3 [y^x] [times] = 4432.99 |

coryrmoore |
Thanks Jonan |

sshetty2 |
I didn't read the question properly, u actually have to calculate the nfv then add the interest for another yr |