Question

Calculate from `e_0^0,e_1^0,e_2^0` from the following data : 

Age x	0	1	2
`l_x`	1000	900	700
`T_x`	-	-	11500

Answer 1

Given` l_0=1000, l_1=900, l_2 =700, T_2=11,500`

We have `L_x=(l_x-l_x+1)/2`

`L_0=(l_0+l_1)/2`

`L_0=(1000+900)/2=950` 

`L_1=(l_1+l_2)/2`

=`(900+700)/2=800` 

We have `T_x=L_x+T_(x+1)`

∴ `T_1=L_1+T_2` 

∴ `T_1=800+11,500=12,300`

`T_0=L_0+T_1` 

`T_0=950+12,300=13,250` 

Now `e_x^0=T_x/l_x ∴ e_0^0=T_0/l_0` 

`∴ e_0^0 = 13250/1000=13.25`

`e_1^0 =T_1/l_1=12300/900=13.667` 

`e_2^0=T_2/l_2=11500/700=16.428`