Question

Calculate `"e"_0^circ ,"e"_1^circ , "e"_2^circ` from the following: 

Age x	0	1	2
lx	1000	880	876
Tx	-	-	3323

Answer 1

We know that  `"e"_"x"^circ = "T"_"x"/"l"_"x"`

Age x	lx	Lx	Tx
0	1000	940	5141
1	880	878	4201
2	876	-	33236

L_x = `("l"_"x" + "l"_("x" + 1))/2` , x = 0,1,2

L₀ = `("l"_0 + "l"_1)/2 = (1000 + 880)/2 = 940`

L₁ = `("l"_1 + "l"_2)/2 = (880 + 876)/2 = 878`

T₂ = 3323 given

T₁ = L₁ + T₂ = 878 + 3323 = 4201

T₀ = L₀ + T₁ = 940 + 4201 = 5141

`"e"_0^circ = "T"_0/"l"_0 = 5141/1000 = 5.141`

`"e"_1^circ = "T"_1/"l"_1 = 4201/880 = 4.7739`

`"e"_2^circ = "T"_2/"l"_2 = 3323/876 = 3.7934`