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Message-ID: <37E111D3.4B7E2AA4@earthlink.net>
Date: Thu, 16 Sep 1999 08:50:43 -0700
From: David Rafferty <rafferty2@earthlink.net>
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To: BrianOhlman <Brian.Ohlman@thehartford.com>
Subject: Re: May 1996 Actex #9
References: <0012900000070970000002L002*@MHS>
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Determining a net single premium simply means calculating the value of the
entire 3-year discrete endowment: 1000A(30:3]
Page 115 of the 1997 Bowers text gives the calculation of an n-year endowment
with a unit amount payable at the end of the year of death as:
n-1
A(x:n] = SUM [v^(k+1)*kpx*q(x+k)] + v^n(npx)
k=0
With force of interest 0.09, v = e^(-0.09)
k
With constant force of mortality 0.12, kpx = exp[ -INTG(0.12dx)] = e^(-0.12k)
0
where INTG denotes the integral symbol
>From this we get q(x+k) = [1 - e^(-0.12)] which does not depend on the value of
k
So our net single premium calculation is:
2
1000A(30:3] = 1000SUM [v^(k+1)*kp30*q(30+k)] + v^3(3p30) =
k=0
2
= 1000SUM [(e^-.09(k+1))*(e^-.12k)*(1 - e^-.12)] + (e^-.27)*(e^-.36)=
k=0
= 1000{(1 - e^.12)*[(e^-.09)*e^0 + (e^-.18)*(e^-.12) + (e^-.27)*(e^-.24)] +
(e^-63)}
= 787.55
The best answer is (A).
I hope this helps. If anyone knows a faster way to solve this problem, please
let me know.
David
..
BrianOhlman wrote:
> Can anyone help out with this one?
>
> Henry, aged 30, is subject to a constant force of mortality, u(x)=.12.
> Henry wants to buy a 3 year endowment insurance, with a $1,000 benefit
> payable at the end of the year of death. You may assume the force of
> interest of .09. Determine the net single premium for this insurance.
>
> -Brian
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