- CFA Exams
- 2021 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)

###
**CFA Practice Question**

Which of the following amounts is closest to the end value of investing $80,000 for 3 years compounded continuously at a rate of 12%?

B. $113,550

C. $114,667

A. $112,750

B. $113,550

C. $114,667

Correct Answer: C

End value after 3 years = 80,000 (1 + 0.1275)

EAR = (e

^{r}- 1) = e^{.12}- 1 = 0.1275 (12.75%)End value after 3 years = 80,000 (1 + 0.1275)

^{3}= $114,667.31###
**User Contributed Comments**
20

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

brimann |
BAII+ Solution .12 continuously compounded = 1.1275 I/Y = 12.75 (1.1275-1) N = 3 PV = -80,000 PMT = 0 FV = 114,667 |

KD101 |
Can someone try it for me using Brimann's method, I am getting 116,922.4145 |

jaan |
Briman's method, EFF=12.7497 (ie calculated above) C/Y = 12 e^log =162754.7914 ENTER CPT NOM = 12.00 Note (C/Y = 12 because countinuously compounding period is 12 months) |

jimmymh |
an easier way would be just, .12*3 then 2nd e^x, times 80,000 |

PeterW2006 |
With continuous compounding, at any time t, the value of a deposit is given by ae^(rt) For this question, a = 80,000 e = 2.71828 r = 12% continuous compounding rate t = 3 years Value = 80,000 x e^(0.12x3) = 114,666.33 |

cptp |
Can somebody explain 12.75%? |

Indira |
EAR=(1+per.int.rate)^m - 1 EAR=(1+0.12/365)^365-1=0.1275 |

mansi |
for continous compounding the formula is (e^r-1) on substituting r=12, you will get 12.75 |

o123 |
ICONV ; NOM=12, C/Y=365 --->EFF= 12.74746 |

mordja |
do yourselves a favour and use jimmymh's method. |

JKiro |
An add on to jimmymh's method:- For an interest that is compounded continuously, the formula to be memorized: FV=PV*e^(r*N) or PV=FV/e^(r*N) where r = rate; N = number of years |

seankang |
hp 12c 1)1enter, 0.12ge* equals 1.1275 2)n3,12.75i,pv80,000,fv114,667 |

SANTOSHPRABHU |
Using BA II Plus: As rate is = 12% = 0.12 EAR (Continuously compounded) = (0.12 ex - 1) = 1.1275 -1 = 0.1275 = 12.75% = I/Y N = 3 PV= - 80,000 FV = $114,667. |

rhardin |
Just make your Number of periods equal 3 x 365 (which is 1,095) in your calculator so there is compounding everyday, and you will still come up with the right answer without having to memorize the formula for continous compounding. Make your I=.12/365 and solve for FV. And you're done! |

jansen1979 |
Great comment by rhardin. Works really easy this way. |

8thlegend |
The question is getting to me. Because we are in the subject of ordinary annuity or annuity due. Isn't the question saying that he or she is investing 80k every year for 3 years? |

Struggler |
Effective Interest Rate = (1+Periodic Interest Rate)^number of periods in a year then - 1 Shout out to ma boy rhardin! |

johntan1979 |
If you don't round (by right you should NOT), it's 114,659.57 |

birdperson |
jimmymh knows whats up |

plammar71 |
Put pmt |