Actuarial Outpost Geometric Series Question
 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

 United KingdomActuarial Jobs General Insurance, Life & Other Areas Canada Actuarial JobsCasualty, Life,Pension,Health & Investment Entry LevelActuarial JobsAll Disciplines Health, Life, Pension, Casualty, Investment D.W. Simpson & Company ActuarialRecruitersWorldwide www.dwsimpson.com

#1
12-07-2011, 11:39 AM
 mhorng Join Date: Jul 2010 Location: Milwaukee, WI Studying for MFE College: Marquette University Posts: 8
Geometric Series Question

In ASM, the formula for the present value of payments in geometric progression (section 4j) has a denominator of (i-k). However, in some of the solutions it uses [1-(1+k)/(1+i)]. When is it appropriate to use either one of these?
__________________
P FM MFE MLC C
Econ Fin Stat
#2
12-07-2011, 12:17 PM
 icon41gimp Member Join Date: May 2011 Posts: 429

The first is dividing by (i-k) the second thing you have is dividing by (i-k)/(1+i) [after doing the algebra]

If you break the second thing into two steps it's dividing by (i-k) then multiplying by (1+i)

I don't have an ASM manual but it looks like they're accumulating whatever they calculating by another period; doing it a slightly concealed way
#3
12-09-2011, 06:36 PM
 Wedge^Product Join Date: Jul 2011 College: SUNY at Buffalo Posts: 8

With (1-[(1+k)/(1+i)]^n)/(1-(1+k)/(1+i)) it's just an n term geometric series with r = (1+k)/(1+i) so you're summing 1 + v + v^2 + ... + v^n (Payments at the beginning of each period)

With (1-[(1+k)/(1+i)]^n)/(i-k) it's the above series multiplied by v = 1/(1+i). So you're summing v + v^2 + ... + v^n (Payments at the end of each period)

Personally, I'm more comfortable just figuring out what r is and using the formula for the geometric series. I feel like it gets you into less trouble because you never pick the wrong formula. Plus there have been some problems where the algebra simplifies neatly when you use v'=(1+k)/(1+i).

Is it odd that I think the hardest part about this exam is the little stuff? The stuff that really screws me up is something like Fund X accumulates from 1/1/02 to 12/31/33. I often don't take the time to think about how many periods it is and just use n=31. Super horrible mistakes ensue.

Last edited by Wedge^Product; 12-09-2011 at 06:43 PM.. Reason: meh
#4
12-09-2011, 10:09 PM
 alphatmw Member Join Date: Jun 2011 Posts: 168

^ i didn't even notice your mistake in n=31 for about 30 seconds lol

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off

All times are GMT -4. The time now is 07:48 PM.

 -- Default Style - Fluid Width ---- Default Style - Fixed Width ---- Old Default Style ---- Easy on the eyes ---- Smooth Darkness ---- Chestnut ---- Apple-ish Style ---- If Apples were blue ---- If Apples were green ---- If Apples were purple ---- Halloween 2007 ---- B&W ---- Halloween ---- AO Christmas Theme ---- Turkey Day Theme ---- AO 2007 beta ---- 4th Of July Contact Us - Actuarial Outpost - Archive - Privacy Statement - Top