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Basic Question 3 of 7

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?

A. $245,732.88
B. $256,592.49
C. $316,549.50
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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
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