Professor Broverman, I had another question from your 2005 Exam M study manual. For question 2 of your Section 19 Exercises on LC226, you find that A50 equals .24467 and the second moment is .1201. For Var(L), you obtain 104,400. However, using the same numbers, I obtain 105,581 and I believe this difference is large enough to question. Am I doing something wrong, or have I made a mistake? Thank you for any clarification.
Sponsored Ads
Pauline Reimer, ASA, MAAA Pryor Associates Actuarial Openings: Life, P&C, Health, Pensions, Finance 
Ezra Penland Actuarial Recruiters Top Actuary Jobs Salary Surveys Apply Bios Casualty Health Life Pension 
Banner Ad 1
Collapse
Announcement
Collapse
No announcement yet.
Question(s) for Professor Broverman
Collapse
X

Godspeed,
You have it right. That was my mistake.
This one is in the errata list, which can be
found at http://www.sambroverman.com
(you said your are using the 2005 edition,
so take that link).
Sam Broverman

Professor Broverman, I have another question that I didn't see addressed in your manual's errata. On LC251, you calculate the benefit premium as 166.56. Yet, in your L formulations, this number fluctuates from 166.53 to 166.60. I'm thinking this is just a typographical error, but I just wanted confirmation. Thanks.act justly. walk humbly. .
Comment

Three more questions, Professor Broverman: 1) In question 14 on LC286, you list a(doubledot)40:10 as 7.6, but in the solution you list it as 7.7. Is the 7.7 figure the correct one? Also, a question on semantics: this same question asks about a 20payment, 35year endowment insurance. Does this mean that premiums are paid for 20 years and the insurance lasts for 35, thereby being unaffected by the 20 payments? It just seems like the test designers try to word as trickily as possible, but maybe it's just me.
2) For part b) in question 23 on LC288, I attempted to use the k=20 line to find Px from the relationship kVx=Ax+kPxa(doubledot)x+k
Solving for Px, and using the Ax=1d*a(doubledot)x relationship and the values on the k=20 line, I obtain:
Px=(Ax+kkVx)/a(doubledot)x+k
=(1.06*1.06*11.145.24782)/11.145
=.01089
, which is exactly a tenth of the size of the answer you give as .1089. I believe the correct premium should be .01089.
3) In the solution of question 31 on LC298, you calculate abar50:10 as 6.5787. Yet, using the same numbers, I get 6.594, changing the final answer to 95.96.
Your continued help is greatly appreciated. Thank you.Last edited by .Godspeed.; February 9 2006, 09:23 PM.act justly. walk humbly. .
Comment

Godspeed,
In LC286 #14, the annuity value of 7.60 should
have been 7.70, and in LC288 #23 you are also
right that the premium should be .01089 .
Thanks for poitning those errors out. I have
addedn them to the online errata list at my
website.
REgarding the use pf the phrase "npayment insurance
policy". This means that the policy has up to n scheduled
premiums (if the policyholde lives that long), but the premiums
would stop if death occurred before time n.
For instance, a 30payment whole life insurance refers
to a policy with premiums for up to 30 years, but if the
policyholder lives longer than 30 years, the policy continues
but no more premiums are paid. Of course, this means
that the premiums would be larger than if they were payable
for whole life on the policy, so the policy can be paid
off earlier. There is standard actuarial notation to
represent an "npayment policy". If the premium symbol for
a policy with premiums for the full lifetime of the policy is P,
then the npayment premium policy with the same death
benefits is denoted nP (where the n one the left is a
subscript). So for the 20payment, 35year endowment
policy you mentioned, the premium could be denoted
20 P x:35 . This can be confusing when there
is the nyear survival probability n p x, but the p is lower
case for the survival probability and capital P for
the premium notation.
Sincerely,
Comment

Thank you very much; that cleared it up.
It appears that you replied as I was editing my post, so here is the last question I had that your probably didn't see:
3) In the solution of question 31 on LC298, you calculate abar50:10 as 6.5787. Yet, using the same numbers, I get 6.594, changing the final answer to 95.96.
Also, on LC299, on the line reading "but it is not always true that", I believe the "" should be a "=".
Thanks again.Last edited by .Godspeed.; February 11 2006, 05:48 PM.act justly. walk humbly. .
Comment

Thanks for the updated errata.Last edited by .Godspeed.; February 15 2006, 12:30 AM.act justly. walk humbly. .
Comment

Professor Broverman, I had a question regarding your August 1, 2005 Exam M Question of the Week. I spotted what look to be two transcription errors: 20E35 should be .286 and not .266; and 2^A35 should be .03488 and not .3488.
I now get E(S)=27420*1000 and Var(S)=656,890,715*1000.
Using these updated values, I now get a desired premium of 28,459 as opposed to 24,740. Could you please confirm this? Thank you very much.act justly. walk humbly. .
Comment

.Godspeed,
I think your formulation for E[W^2] is incorrect.
W pays a death benefit of 200,000 for death prior to 65
and 100,00 for death after 60. Then W^2 wouldpay
200,000^2 prior to 65 and 100,000^2 after 65 (with a
doubled force of interest for present value calculation).
You have written
E(W^2)=200,000^2*2^A35100,000^2*30p35*v^60*2^A65 .
This would pay 200,000^2 for whole life, but then 100,000^2
would be cancelled off for death after age 65. This results in
200,000^2  100,000^2 paid for death after age 65,
but the payment should be 100,000^2 (which is not equal
to 200,000^2  100,000^2). Thiis formulation worked for E(W)
since 200,000  100,000 = 100,000 .
Sincerely,
Sam Broverman
Comment

Ok, I deleted the previous post so others might not be confused. I think I have it now. I think I was trying to take a shortcut without fully checking my logic.
We agree that E(S)=1000*E(W)=19,620,000.
E(W^2)=200,000^2*(2^A35v^60*30p35*2^A65)+100,000^2*v^60*30p35*2^A65
=200,000^2*(.03488*1.06^60*7533964/9420657*.23603)+100,000^2*1.06^60*7533964/9420657*.23603
=1,223,536,132
Var(W)=E(W^2)E(W)^2=1,223,536,13219,620^2=838,591,732
Then, Var(S)=1000*Var(W)=838,591,732,000
Thus, (1000C19,620,000)/sqrt(838,591,732,000)=1.282>C=20794
Is this better? Thank you for the continued help.Last edited by .Godspeed.; March 11 2006, 01:31 PM.act justly. walk humbly. .
Comment
Comment