ASSURANCES ON LIVES.
15/
the annual premium is therefore (l—r), and since —p- is the
single premium, this quantity divided by (1 + #™) is
Mm 1 _ M m D,„ _ M m
D ))t ' 1 +a m D m ' N m _, N m _i’
which is also the formula.
Rule (1). The single premium is found by adding one to the present
value of .the annuity on the given life or lives, multiplying the sum by
the difference between unity and the present value of £l due at the end
of one year, and subtracting the product from unity.
Or, (2) Multiply the annuity by the annual interest,of ¿£l, subtract
the product from unity, and divide by the amount of ¿£l in one year.
By Davies’s method :
(3) Divide the number opposite the age in column M by the number
opposite the age in column D.
Or, (4) Divide the number in column N opposite the age one year
younger than the given life by the number in column D opposite the
given age, multiply the quotient by the difference between unity and the
present value of £l due in one year, and subtract the product from
unity.
To find the annual premium ;
(1) Divide the single premium by the annuity on the given life or
lives increased by unity.
Or, (2) Divide unity by the present value of the annuity increased
by unity, and from the quotient subtract the difference between unity
and the present value of £l due in one year.
By Davies’s method:
(3) Divide the number opposite the age in column M by the number
opposite the age one year younger in column N.
Or, (4) Divide the number opposite the age in column D by that
opposite the age one year younger in column N, and from the quotient
subtract the difference between unity and the present value of £l due
in one year.
192. Construction of column M, Carlisle 4 per cent.
<W- 10 H w .r 100 .r 5 = 1 X .01980004 X .82192711 = .016274190=M 10 <
d m r m =(l m -l m )r m .r*= 2 X .01980004 X .85480419= .033850312
.050124502 = Mi 0S
d m r l0 Hl m -l m )r m .r 3 = 2 X .01980004 X .88899636=.035204326
.085328828=M 10a
2 X .01980004 X .92455621 = .036612500
J21941328=M 10 ,
