- CFA Exams
- CFA Exam: Level I 2021
- Study Session 2. Quantitative Methods (1)
- Reading 6. The Time Value of Money
- Subject 3. The Future Value and Present Value of a Single Cash Flow

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**CFA Practice Question**

You expect to receive a lump sum distribution of $285,000 from your pension plan in 18 months. Assuming continuous compounding at an annual rate of 7%, what is the present value of the distribution?

B. $256,592.49

C. $316,549.50

A. $245,732.88

B. $256,592.49

C. $316,549.50

Correct Answer: B

In continuous compounding, N is the number of periods of compounding at the per period rate, r. In this case, r=7% per year, and N=1.5 years.

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**User Contributed Comments**
38

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

vincenthuang |
my answer is $257,495.23 r=7% N=1.5 FV=285,000 |

brimann |
My answer (-.07x1.5) = -.105 using BAII+ continuous compounding function = .9003 x 285,000 = 256,592.49 |

lna1717 |
my answer is to compute EAR =(1+7%*18/12)^(18/12)then FV/EAR=285000/1,1615=245358 |

fuller |
brimann's explanation is correct. So is the answer. |

synner |
EAR=(1+r/m)^(m*n) m is # of compound period per year, 18/12=1.5 n= # of years, which is 18 month = 1.5years. so EAR = (1+.07/1.5)^(1.5*1.5) = 1.108 FV/EAR= 285000/1.108=257202.97 Using another method, set C/Y = 18/12=1.5, using BAII plus, 2nd P/Y arrow down to C/Y, and set it to 1.5, then N=1.5 FV=285000, PMT = 0, I/Y=7, CPT PV = 257202.97 I'm confused, anyone explain? btw, C/Y is compound per year. and P/Y is payment per year. |

Aish |
I know that brimann's explanation is correct, but can anyone tell me why? Also, what are we using for the interest and # of periods? I keep getting the wrong answer. |

nhla |
285000 * e^(-0.07*1.5)where 1.5 years is the 18m 285000 * e^(-.105) 285000*.90032 = 256,592.49 |

Will1868 |
I like nhla's answer best - remember the question mentioned "continuous" compounding |

aguns |
i agree that nhla's answer is best. take not of the word "contionous" |

stefdunk |
How do we do this calculation on the BA II+? |

Haiqing |
when u using BA II+, just check the BEST answer |

Done |
Remember to CLEAR YOUR CALCULATOR ALWAYS!!! |

Jay |
what's the continuous compounding function on BAII+? |

chuong |
only 1 way N=1, I/y = e^(-0.07*1.5) FV=285000 =>PV = ??? |

Chitu |
The problem can be sloved using [ICONV] function in BAII+. 2nd [ICONV] NOM=7 C/Y=1.5 EFF=? The outcome is EAR = 7.08 Substituting I/Y=7.08 N=1.5 FV= 285,000 PV=? PV=256908.33 However there is a difference of $315.84 |

PedroEdmundo |
a closer answer would be to to put: N=365*1.5 FV=285000 I/Y=7/365 |

akanimo |
i cannot see how in the world "continuous compounding" can be equated to compounding once a year! ... for my bank it means compounding "daily" or at worst "monthly" ... definitely not once a year ... so i would expect n = 360 (days) or n = 365 (days) or at worst n = 12 (months) and the interest rate recomputed along the value of n |

akanimo |
actually should have written n = 360 x 1.5 (days) or n = 365 * 1.5 days or n = 12 * 1.5 months ... my error. |

yakubovich |
EAR (for year) = (e^0.07) - 1 = 0.0725 PV = 285000/((1+0.0725)^1.5) = 256592 |

Mattik |
Key point = "continuous compounding" Therefore, you should use: PV = FV/e^(r*N) = 285,000/e^(.07*1.5) = 285,000/e^.105 = 285,000/1.11071061 = 256,592.4889 |

guai |
Totally agree with Mattik. "continuous compounding" is the key, not daily or monthly. |

o123 |
I like Chitu's explination: but with a slight adjustment cause I also whole heartedly agree with akanimo. ICONV; NOM=7, C/Y=365 --> EFF= 7.25 FV=285000, I/Y=7.25, N=1.5 (18 months)-->PV=256595.07 |

nads2007 |
I think mattik's explanation is the way to go thanks mattik |

arwen |
yes,continuous compounding is the key, greater value will be achieved at the end of period.e^(n*r)is involved |

KSHO |
BA II Plus 2ND CLR TMV .07 2ND LN (e^x) = 1.072508 (EAR) I/Y = 7.2508 N = 1.5 FV = 285000 CPT PV = -256592.55 (rate was rounded) |

ravdo |
Can anyone pls explain step by step on HP12C calc? |

TammTamm |
Pedro, i like the method you presented first. it's easier to calculate. thanks |

JKiro |
Using HP12c: first remember the equation for continuous compounding: PV = FV / e^(r*N) where r is the rate and N is the number of years. Back to HP12c: calculating first the (r*N) value and taking the exponent (0.07*1.5) = 0.105 0.105[g][e^x] = 1.11071 moving the answer to the denominator 1.11071[1/x] = 0.90032 multiplying by the distribution amount 0.90032*285,000 = 256,592.48 |

SANTOSHPRABHU |
PV of the distribution assuming continuous compounding at an annual rate of 7% = PV = e^ (-0.07X 1.5) X 285,000 = 0.900325 X 285,000 = 256,592.4889 |

josie491 |
take note of key word "continuous compounding" -- use formula PV=e(-0.07x1.5)x285,000=256,592.49 |

tovamst |
? Press [2nd] [P/Y], input 1, then press [ENTER]. ? Press the [down arrow] key, input 1,000,000,000, then press [ENTER]. NOTE: Inputting a very large value for the number of compounds per year (C/Y) is an approximation of infinity, resulting in continuous compounding. ? Press [2nd] [QUIT] to return to the home screen. ? Input 1.5, then press [N]. ? Input 7, then press [I/Y]. ? Input 285,000, then press [+|-] [FV]. ? Press [CPT] [PV]. |

robbiecow |
You could also just hit on the BA r = exp(.07) n = 1.5 pmt = 0 fv - 285,0000 |

lordcomas |
I totally agree with PedroEdmundo, great answer and easiest way to input the data into the calculator. Thanks Pedro. |

NBlanco |
if using 12C see JKiro answer |

jjh345 |
for BA II Plus: FV: 285,000 PMT: 0 IR: .583 (7/12, because the date is given in months, divide your interest rate by 12) N: 18 ( 18 months) |

gtokarz |
You all are making this too complicated. Simply do the following. 0.07*1.5 = 0.105 Then take 0.105> 2nd LN > which equals 1.11071. Now discount the FV by that, ie: 285000/1.11071 = 256,592.63 , just pennies off |

ravinkalu |
gtokarz is correct because FV=PV * e^(r*N) or PV = (FV) / e^(r*N) $285000 / e^(.07*1.5) e^(.07*1.5) = 1.11071 |

kimmykim23 |
Formula for continuous compounding is FV = PVe^(r*N). Therefore, 285,000=PVe^(.07*1.5) e^(.07*1.5) = 1.1107 285,000=1.1107PV PV = 256,592.49 |