214 
LIFE ASSURANCES, 
the annual premium for the’same is 
A — 
(m, mj) 
(1-r). 
) ul 
1 ”1” ^m “f” ti rn ^ (tm, m 1 1 "i" T* ^m\ mi 
The single premium for an assurance on the last v survivors of any 
number of lives aged m, m u m 2 , &c., is 
r— (1—r)a 
(m, tîi\, m2, &c.) 
or 1 —(1— r)(l + a 
(m, mi, m-2> &c.) 
(m, m\, m% &c.) 
1 -ia v — 
v qj* (m, Wp m2, &c.) 
the annual premium will be 
^ — 
m, m l5 m2, &c.) 
1 + a 
l+i 
(m, m^ m2, &c.) 
1 + a. 
(1-r). 
(m, mi, m£, &c.) 
TEMPORARY ASSURANCES. 
The single premium for an assurance for n years on a life aged m is 
A (m) ^ — r. 11 - yt"r n J - (1 — r) (« m — ^ r". 
° r D m 
the annual premium is 
r (N m _! ~ N m+n _,) — (N m - N m+n ) 
D„ 
A 
(m) 
ni 
'm I'm 
'm-f-n 
L 
1 - —r +a m — —^ r n .a n 
m v m 
-(l-r). 
N m _!—N,,^’ 
N -N 
x ' m ^ m+n 
or r “N—Tn • 
The single premium for an assurance for n years on two joint lives 
aged m and m 1 is 
A — rl 1 l ,n+n ^ mi+n r n \ n (n L + n . \ , 
(m, my) 7 * / ‘ r \-** ’ JKy'm, my t / ?wi-|-n/ j 
7i ^ t ^m.j J ^m-i 
the annual premium is 
A ( m , >»,) 
nl 
1 
'm+n 
n n , __ ^-f 7 * ^n-t- 77 
/ 7 “T a m, mi j * j 
''in. ' J 'rn v« 
I'm+n 
m\ +n 
l ’m\ 
-, ^m 1 -f-w « , 
1 -lZ'T7 r+a - 
m-fn ^my-\~. 
-(1-r). 
A, 
L 
1 mi+w