356 Practical Comparison of 



L. Three joint lives, at 5 per cent., compared with the Carlisle 

 tables. 



Common age. Daily payments. Annual payments. Carlisle tables. North, tables. 



30 11.37 10.87 10.82 (8.50) 



33. For the arithmetical hypothesis, the computation becomes still 

 more simple, and requires no auxiliary tables beyond those which 

 are universally known. The contingency for the three joint lives 



here becomes ^ \P '^ V ) "^ PP — '_ and the value, taking 



A', A''', A'^' for the existing tabular values of 1, 2, and 3 lives at the 



age of the eldest^ iLAi- ^L2 £-£. — ^^'andp" being 



rC rC 



the excess of the elder above the two younger respectively, divided 

 by c : we might also add half a year to the tabular numbers, and 

 deduct it from the final result, if necessary. 



34. The same simplification is applicable to two joint lives, the 



s s 1) n s 



contingency becoming — . — r= — s (s + i_) := ss + ~J- — . 

 k k' kK c kh! 



and the values — -_ + — 



k' ck' 



M. Two joint lives, at 4 per cent., from the equal lives. 



