Question

Calculate quantities indicated by'?' for the following part of a life table : 

x	lx	dx	qx	Lx	Tx	`e_x^0`
4	9100	60	?	. ?	510000	?
5	?	45

Answer 1

Using `d_x = l_x - l_(x + 1)`

`l_(x + 1) = l_x - d_x`

`l_5 = l_4 - d_4`

∴ `l_5 = 9100 - 60`

∴ `l_5 = 9040`

Using `q_x = d_x/l_x`

`q_4 = d_4/l_4 = 60/9100`

= 0.0066

Using `L_x = (l_x + l_(x + 1))/2`

`L_4 = (l_4 + l_5)/2 = (9100 + 9040)/2 = 18140/2`

∴ `L_4 = 9070`

Using `e_x^0 = T_x/l_x`

`e_4^0 = T_4/l_4 = 510000/9100`

= 56.04