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209 
RECAPITULATION OF FORMULAS. 
NOTATION. 
ci m — present value of ¿£l per annum on a life aged in. 
^ m, mi, m2, &e, — do. on the joint existence of the lives aged 
m, m,, m 2 , &c. 
do. on the joint existence of the last v survivors 
of the lives aged m, m,, m 2 , &c. 
»resent value of £\ per annum for the next n years, 
subject to the existence of a life aged m. 
do. subject to the joint existence of the lives 
aged m, m,, in 2 , &c. 
do. subject to the joint existence of the last v 
survivors of the lives aged m, m,, m 2 , &c. 
»resent value of £l per annum to be entered upoa 
at the expiration of n years, and afterwards to 
continue so long as a life now aged in shall sur 
vive that period. 
¿hm,mi, m 2 , &c.) — do. dependent on the joint existence of the lives 
now aged in, in,, m 2 , &c. 
— do. on the joint existence of the last v survivors 
1,1 of the lives aged m, in,, m 2 , &c. 
A substituted for a in each of the above cases, denotes the present 
value of an assurance of ¿£l for a similar term. 
A m , = present value of an assurance of £l on the failure of 
a certain life aged in, provided another aged in, 
survive him. 
esent value of an assurance of £ 1 on the death of 
a party aged in, provided another aged m, shall 
have died previously. 
esent value of an assurance of £l payable at the 
end of the year when a life aged in shall fail, pro 
vided that event happen within the next n years, 
and another life aged m, survive him. 
do. provided the event happen after the next n 
years. 
d m — the number dying in the with year of age. 
e m — average number of years a life aged m survives, 
called the expectation. 
l m = number of living at the age rn. 
'in