220 
LIFE ASSURANCES. 
The annual premium for the same will be 
(r/-p)(M„ 1 -M ? „ +n ) + p (R,„ - R m+ „ — n. M„, f „) 
The single premium for a similar assurance, decreasing £p annually, 
will be » 
(a +p) (M m - M m+n ) —p(R m — R m+M —n. M m+ „) 
D m 
Tire annual premium will be 
(a +p)(M m —M m+B ) — p(R,„ -R m+ „-n, N„, + „) 
h^m-fn—l 
v The single premium for an assurance for the whole term of life, com 
mencing at £a and increasing £p each year will be 
(a-p) M m -f p. R ,„ 
Dm 
The annual premium will be 
(a —p) M m +p. R m 
Nrall ’ 
The single premium for a similar assurance, decreasing £p each year 
will be 
(a+p)M m —p.R m „ ; 
Dm ' ' 
The annual premium will be 
(a+p) M nl — p ■ R„, 
N m _i 
ENDOWMENTS, ANNUITIES, AND ASSURANCES, 
With return of premiums in case of Death. 
The annual premium to secure £l to be received at the end of n years, 
provided a life aged m survive that terra, or in the event of his dying 
before that time all the premiums to be returned at the end of the year 
in which he shall cease to exist will be 
Nm-I + Rm+J. + — N„, +n -i — R m 
The annual premium to secure £l per annum to be entered upon at 
the expiration of n years, subject to the existence of a life now aged m, 
or in the event of his dying before that time the premiums to be re 
turned at the end of the year in which the existence shall fail, will be