Actuarial Outpost C2: TOI Question
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#1
10-01-2002, 09:54 AM
 shluffer Member CAS Join Date: Aug 2002 Posts: 489
C2: TOI Question

From SOA 140 May 1991:

Given: (i) a(bar,10) = 7.52
(ii) d/ddell a(bar,10) = -33.865.

calculate d
The aswers are
(a) .059
(b) .060
(c) .061
(d) .062
(e) .063

when I solve for dell I get .059997581. when i use e^(dell) = (1-d)^(-1) to sove for d i get d = .05823. the answer in the solution manual I have is .06, which is what I am getting for dell. is this a typo in the manual (should be solving for dell) or am i doing something wrong?
#2
10-01-2002, 10:10 AM
 retaker Member Join Date: Aug 2002 Posts: 395

I got the same thing you did.

Delta is .06 d= .058235466

I approximated delta, though. How did you solve for delta?
#3
10-02-2002, 12:36 PM
 shluffer Member CAS Join Date: Aug 2002 Posts: 489

e^(dell) = (1-d)^(-1)
#4
10-02-2002, 12:40 PM
 retaker Member Join Date: Aug 2002 Posts: 395

yeah, I know that, but wasn't there an equation :

(e^delta)= delta + c

#5
10-02-2002, 03:52 PM
 shluffer Member CAS Join Date: Aug 2002 Posts: 489

when I solved it I didn't end up with a constant. Where did you take an integral?
#6
10-02-2002, 03:57 PM
 retaker Member Join Date: Aug 2002 Posts: 395

I didn't do an integral, the equation I set up to solve for delta had an e to the delta term plus or minus a plain delta term. I don't believe there is a nice way to solve for delta nicely in this situation. Do you remember what equation you solved to get delta? Maybe you had a nicer way to solve for delta?
#7
10-02-2002, 04:12 PM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 26,458

Method 1:

If you use both given i and given ii, you get two equations that involve e^(-10delta) and delta. In the equation for given i, solve for e^(-10delta) in terms of delta.

Substitute that formula for e^(-10delta) in the equation for given ii. It turns out to give a linear equation in delta.

Method 2:

Under exam conditions, the fastest way to do this problem would be to try the possible answer choices until you found the one that gave you 7.52 for the 10 year annuity.

Method 3:

Could you approximate delta as i upper 100? Store in calculator 1000 payments of 0.01 each, present value = 7.52, solve for i.

Calculator hopefully says 0.059946% (0.00059946) per period so i upper 100 is 0.059946; how different could delta be?

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