- 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**

What is the future value of the following annuity due?

Payment frequency = annual, at the beginning of each year

Number of payments = 20

Interest rate = 8% per year

B. $4,576.20

C. $4,942.29

Payment amount = $100

Payment frequency = annual, at the beginning of each year

Number of payments = 20

Interest rate = 8% per year

A. $2,000.00

B. $4,576.20

C. $4,942.29

Correct Answer: C

(Or use the formula to calculate.)

FV = 100(1.08)

^{20}+ 100(1.08)^{19}+ 100(1.08)^{18}+ ... + 100(1.08)^{2}+ 100(1.08)^{1}= $4,942.29(Or use the formula to calculate.)

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**User Contributed Comments**
21

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

Laurel |
Huh? Why would you use the long way instead of the formula? Can't get the formula to give me the right number. |

tawi |
I am not getting the correct answer using the formula |

Jeden |
The formula gave me 4,610.73 FV20 =100(1 + 0,08)^20 + FV19 formula for regular annuity fon N-1 payment What's wrong? |

nic306 |
The formula for annuity due for both FV and PV is the same as regular annuity but multiplied by (1+r) Annuity due = ordinary annuity formula x (1+r) |

KD101 |
I get $4576 from a formula FV = A x [{(1+r)^N - 1}/r] = 100 x [{(1.08)^20 - 1}/0.08] = $4,576 Multiply it with 1+r = 1.08 and we get $4942.29 The multiplcation is due to the fact annuity due starts from t=0. |

tymao |
the future value of annuity due is at the end of 20 or beginning of 21, the same place as 20 normal annuity. that's way 4942 instead of 4576 |

lna1717 |
I ve got 5042 ...using the maths formula A*((1+R)^(N+1))/R FOR N from o to N. whats wrong ? or 4576 + 1,08^20=5042 |

timspear |
The question does not really say at what date in the future it wants the value for. At the time of the last payment you would have 4576 and one year later you would have 4942. |

Sandy69 |
Use Calculator : Set BEG , N= 20, PMT =-100, 1/Y = 8 FV = 4942.29 |

suraj |
FV (ordinary)=PMT[(1+r)^n -1] *1/r FV (Due) =FV (Ordinary)*1+r |

Will1868 |
No kidding - buy the calculator they let you use them! |

hagi10 |
why do you loose time with these formulas? it took me 14 seconds to find the answer on the calculator.... |

Done |
Read the question, "Annuity Due" which means BGN on calculator! |

chuong |
set the BGN mode N=20, PMT=-100, I/Y=8, PV=0=>FV=4942.29 |

Nathan |
To avoid adjusting the settings of your calculator to annuity due (2nd [BGN] 2nd [SET]. You can perform the calculation and then multiply by (1 + r). |

SamehHassan |
it is very easy by calc :) |

Sumit14 |
Future Value of Annuity Due = Future value of Ordinary Annuity * (1+r) So for above question N=20 I/Y = 8 PMT = -100 CPT FV = 4576.20 (i.e. FV of ordinary annuity) multiply it by (1+r) = 1.08 so FV of Annuity Due = 4576.20 *1.08 = 4942.29 |

Emily1119 |
I still can't not find the anwser. How to set the BGN mode and then get the anwser of 4942.29？ |

nabilhjeily |
after we get the fv how do we calculate it on the hp i put the answer x 1.08 & then what |

lordcomas |
Don't forget to (CLR TVM) before entering the values. then solve. |

Sm7272 |
Can we not compute just by pressing FV and changing mode to beg on HP 12 c ? All the other values were entered while solving Q2. I get 0 if I CPT without clearing the registers. Does HP 12C not retain values once PV is computed ? |