kPx
Qx+k , for k := 0,1,2
For the first term, I used the definition of kPx:
kPx := exp {-INT [u(x+t)dt]} , limits 0 <= t <= k
= exp {-INT [0.12 dt]}
= exp {-0.12k} (1)
Which doesn't depend of the age x
The second is the same. If Qx+k = 1 - Px+k, then the expression in (1) may
be used to find Px+k:
Px+k := exp{-0.12} ==> Qx+k = 1 - exp{-0.12}
There's an easier third thing: translate the force of interest into the
discrete v^k. That would be v^k = exp{-0.09k}
Finally, the net single premium for the endowment insurance would be:
2
SUM [exp{-0.09(k+1)}exp {-0.12k}(1 - exp{-0.12})]
k=0
+ exp{(3)(-0.09)}exp {(3)(-0.12)}
After the algebra, I came up with:
1 - exp{-0.63}
(1-exp{-0.12})(exp{-0.09}) ---------------- + exp{-0.63}
1 - exp{-0.21}
Agree, anyone?
> -----Mensaje original-----
> De: BrianOhlman [mailto:Brian.Ohlman@thehartford.com]
> Enviado el: Jueves 16 de Septiembre de 1999 08:07 AM
> Para: - *studygroup4a@lists.casact.org
> Asunto: May 1996 Actex #9
>
>
> 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
>