CFA Practice Question
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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?
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.
User Contributed Comments 38
|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.|
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
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
I/y = e^(-0.07*1.5)
=>PV = ???
|Chitu||The problem can be sloved using [ICONV] function in BAII+.
The outcome is EAR = 7.08
However there is a difference of $315.84
|PedroEdmundo||a closer answer would be to to put:
|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)
|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|
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:
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
PV = 256,592.49