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Basic Question 3 of 13
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
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 |
I am using your study notes and I know of at least 5 other friends of mine who used it and passed the exam last Dec. Keep up your great work!
Barnes
Learning Outcome Statements
calculate and interpret annualized return measures and continuously compounded returns, and describe their appropriate uses
CFA® 2024 Level I Curriculum, Volume 1, Module 1.