1 _ m + '* , m l+ n ~n\ n tm + n , < ’ l, -+ ra r n n 
1 I ' I u 'm, 771! . / * ' U ' m + n * w*i+n 
“m i *'m "mi 
the annual premium payable during the whole period of joint existence 
is 
A 
yi (m, 77i j) 
SURVIVORSHIP ASSURANCES. 
The single premium to assure a sum payable on the failure of a life 
aged m, provided another aged mj survive him is 
mi '— ^'^■‘^ni, nij i 1 ®i»-l|«iij) 
1 { A , Gm—1, t«i —1 t 
o < i ’ ( j 
2\ Pm-1,1 Pirn-!,! 3 
or when ??i—1 is greater than m i ? 
, WJ-1+ N777,—-1, 771 1 
1 f J ^ ^ (-N777.— 1, 771J —1*4“ ^777— 1, 771! 
or when ?/?!—1 is greater than m, 
(him—1, N«.-., mi ) — 7 ( h\ rn—I, mj—1 “ hi,„ ( mi _j) 1 
the annual premium for the same is 
1 “H )»j 
or when 7/i—i is greater than ?n,, 
1 J W j ”h ^ (him—i, raj—i “I - hi m —1, m j) (hi m —] t rn]—1 “I - N,„ ( mi _i ) j' 
2 1 , 
or when vi x — 1 is greater than m, 
1 j U«i, »n-h 7 (hi m _i.jnj—1 N m> OT ,_! ) hi m —i j —1 ~j-N m _i, m| "I 
21 J’ 
The single premium to assure a sum for n years to he paid on the 
failure of a life aged t/i, provided another aged m x survive him is, 
a.