CONTENTS, 
IX 
Art. 
137, To find the value of a temporary annuity on a single life 
] 40. To find the annual premium to secure a deferred annuity 
Single and Annual Premium for Endowments : 
142. To find the single and annual premium for an endowment 
137 
Page 
certain 
. 109 
certain 
. no 
the end 
be then 
. . HI 
the end 
en lives 
. • HI 
number 
. H2 
or more 
. . 112 
ig within 
number 
life 
fe le lives 
R 
r chase 
ain number 
le life 
112 
158. 
112 
159. 
161. 
113 
114 
162. 
116 
117 
163. 
118 
119 
164. 
165. 
120 
178. 
121 
121 
122 
For Lij 
. 123 
187. 
188. 
189. 
. 125 
Annuities on Two or Three Lives : 
144. To find the value of an annuity on the longest of three lives 133 
145. To find by approximation the value of an annuity on three 
joint lives . . . . . . . ,133 
146. To find the value of an annuity on the longest of two lives . 133 
148. To find the value of a deferred annuity on the longest of three 
lives ......... 134 
149. To find the value of a deferred annuity on the longest of two 
lives . 135 
151. To find the value of a temporary annuity on any number of 
lives 136 
152. To find the value of a deferred temporary annuity , . 136 
154. To find the annual premium for the same . . . .137 
156. To find the value of an annuity payable so long as two out of 
three lives shall be jointly in existence . . . ,138 
Survivorship Annuities: 
To find the value of an annuity on one life after the decease 
of another . . . . . , . . .139 
To find the annual premium for the same . . . .139 
To find the value of an annuity payable during the joint lives 
of A and B, and also during t years after the death of B, 
provided A shall live so long . . , . .140 
To find the value of an annuity on a life A, after the failure 
of the joint existence of two other lives, P and Q . .141 
To find the value of an annuity on a life A, after the death of 
the survivor of two others, P and Q . . . ..141 
To find the value of an annuity on the joint lives of A and B, 
after the death ofP. . . . . . .141 
To find the value of an annuity on the survivor of two lives, 
A and B, after the death of P . , . . .141 
To find the probability that one in particular, of two joint 
lives, A and B, shall die before the other , , ,151 
ASSURANCES. 
e : 
To find the value of an assurance on the last v survivors of 
any number of lives . . . . . . .154 
Expression for the single premium on one life . . . 155 
To find the value of an assurance on one life by Davies’s 
method 155