SoA MLC # 242
For a fully discrete whole life insurance of 10,000 on ((x)), you are given:
* (~_{10} AS =1600) is the asset share at the end of year 10.
* (G = 200) is the gross premium.
* (~_{11} CV =1700) is the cash value at the end of year 11.
* ( c_{10} = 0.04) is the fraction of gross premium paid at time 10 for expenses.
* (e_{10} = 70) is the amount of per policy expense paid at time 10.
* Death and withdrawal are the only decrements.
* (q_{x+10}^{(d)} = 0.02 )
* (q_{x+10}^{(w)} = 0.18 )
* (i = 0.05)
Calculate (~_{11} AS ), the asset share at the end of year 11.
Solution.
At the beginning of the year, the asset share plus net income available is
begin{eqnarray*}
~_{10} AS + G(1-c_{10}) – e_{10} = 1600 + 200(1-0.04) – 70 = 1722.
end{eqnarray*}
At the end of the year, funds must be sufficient to pay those who survive, die and withdraw:
begin{eqnarray*}
& & p_{x+10}^{(tau)} ~_{11} AS + 10000 q_{x+10}^{(d)} + ~_{11} CV q_{x+10}^{(w)} \
&~~~~~~~~=& (1 – 0.02 – 0.18) ~_{11} AS + 10000 (0.02) + (1700) (0.18) \
&~~~~~~~~=& 0.8 ~_{11} AS +506.
end{eqnarray*}
Thus, with (i = 0.05), we have ((1.05) 1722 = 0.8 ~_{11} AS +506), or
(~_{11} AS = 1627.625).