Actuarial Outpost FM2 Problem
 Register Blogs Wiki FAQ Calendar Search Today's Posts Mark Forums Read
 FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions

 Fill in a brief DW Simpson Registration Form to be contacted when new jobs meet your criteria.

 Financial Mathematics Old FM Forum

#11
05-14-2019, 08:19 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,926

There's a quicker way to get the answer. Calculate the level payment that would have to be made at the end of every second year.

0 FV
-5000 PV
10 N
18.147 I/Y

CPT PMT

Set this equal to X(1+i) + 2X.
#12
05-14-2019, 08:41 PM
 jubair07 Member SOA Join Date: Jan 2016 Studying for Exam IFM College: BEng Aerospace Engineering Posts: 158

Quote:
 Originally Posted by Academic Actuary There's a quicker way to get the answer. Calculate the level payment that would have to be made at the end of every second year. 0 FV -5000 PV 10 N 18.147 I/Y CPT PMT Set this equal to X(1+i) + 2X.
Thanks. That's a much simpler way.

But what I don't get it in this method why the payment of 2009 (X) is moved to 2008 (PMT is assumed on even years) since it started in 2007.

So, 2007 to 2008 is only 1 year but payment period is 2 years. So, shouldn't the first level payment be on 2009? If so, 2X payment earns (1+i) from 2008 to 2009 and then X is added on 2009,

giving it 2X(1+i) + X = PMT

Why is that not?
__________________
Exam P Exam FM IFM
#13
05-14-2019, 10:21 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,926

I messed up. I thought they went X, 2X,..... and not 2X,X.....
#14
05-14-2019, 10:26 PM
 Breadmaker Member SOA Join Date: May 2009 Studying for CPD - and nuttin' else! College: Swigmore U Favorite beer: Guinness Posts: 4,951

Quote:
 Originally Posted by Academic Actuary There's a quicker way to get the answer. Calculate the level payment that would have to be made at the end of every second year. 0 FV -5000 PV 10 N 18.147 I/Y CPT PMT Set this equal to X(1+i) + 2X.
__________________
"I'm tryin' to think, but nuthin' happens!"
#15
05-15-2019, 05:46 AM
 jubair07 Member SOA Join Date: Jan 2016 Studying for Exam IFM College: BEng Aerospace Engineering Posts: 158

Quote:
 Originally Posted by Academic Actuary I messed up. I thought they went X, 2X,..... and not 2X,X.....
Thanks! It works. I get the correct answer 10,571 using 2X(1+i) + X = PMT = 1,118.39
__________________
Exam P Exam FM IFM

Last edited by jubair07; 05-15-2019 at 05:51 AM..
#16
05-16-2019, 08:19 PM
 jubair07 Member SOA Join Date: Jan 2016 Studying for Exam IFM College: BEng Aerospace Engineering Posts: 158

Q: A fund earning 8% effective is being accumulated with payments of 500 at the beginning of each year for 20 years. Find the maximum number of withdrawals of 1,000 which can be made at the end of each year under the
condition that once withdrawals start they must continue through the end of the 20-year period.

I solved the problem by letting the fund accumulate with payments of 500 for 20 years and then withdrawing from beginning of 20th period/end of 19th period. It gave me answer of 14 which is what's on the book.

My question is what does they must continue through the end of the 20-year period means?

Does it mean the withdrawal has to start before the end of 20th period or the withdrawal has to start in such time so as the 14 withdrawals of 1000 must finish within the end of 20th period (hence starting at the beginning of 7th period max)?

Or just withdrawals are allowed to go over 20th period and hence up to the end of 33rd period in my case?
__________________
Exam P Exam FM IFM
#17
05-16-2019, 09:47 PM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 31,287

Quote:
 Originally Posted by jubair07 Does it mean the withdrawal has to start in such time so as the 14 withdrawals of 1000 must finish within the end of 20th period (hence starting at the beginning of 7th period max)?
This
#18
05-17-2019, 10:25 AM
 jubair07 Member SOA Join Date: Jan 2016 Studying for Exam IFM College: BEng Aerospace Engineering Posts: 158

Quote:
 Originally Posted by Gandalf This
Thanks mate!
__________________
Exam P Exam FM IFM
#19
05-20-2019, 10:54 AM
 jubair07 Member SOA Join Date: Jan 2016 Studying for Exam IFM College: BEng Aerospace Engineering Posts: 158

Given that δ(t) = 2/(10+t); t ≥ 0; find a4.

My approach: 1+i = e^δ(t)

So, a4= v + v^2 + v^3 + v^4

= 1/e^(2/11) + 1/[e^(2/11*2/12)] + 1/[e^(2/11*2/12*2/13)] + 1/[e^(2/11*2/12*2/13*2/14)]

But answer on the book : a4 = summation of(k=1 to 4) [10/(10+ k)]^2

Where did I go wrong?
__________________
Exam P Exam FM IFM
#20
05-20-2019, 11:11 AM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 31,287

Quote:
 Originally Posted by jubair07 Given that δ(t) = 2/(10+t); t ≥ 0; find a4. My approach: 1+i = e^δ(t) So, a4= v + v^2 + v^3 + v^4 = 1/e^(2/11) + 1/[e^(2/11*2/12)] + 1/[e^(2/11*2/12*2/13)] + 1/[e^(2/11*2/12*2/13*2/14)] But answer on the book : a4 = summation of(k=1 to 4) [10/(10+ k)]^2 Where did I go wrong?
1+i = e^δ(t) Is an expression valid only for the value of 1+i at the the moment of time t. Since delta and hence i are changing continuously, it is not the case that the discount factor for year 1 is equal to e^(2/11). You have to solve for the discount factor by integrating. Similarly for later periods.