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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 |
Solution
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`
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