Life expectancy, or the expectation of life, is the average future lifetime for a person aged 𝑥. It is based on the probability of survival from the current age 𝑥 to each future age from age 𝑥 + 1 to the end of the mortality table.
General formula
The probability of survival 
is the
probability that 𝑥 will survive at least 𝑡 years in the future.
The joint
probability of survival 
is the
probability that both 𝑥 and 𝑦 will survive
at least 𝑡 years in the future.
The last
survivor probability of survival 
is the
probability that either 𝑥 or 𝑦 will survive
at least 𝑡 years in the future.
Life expectancy is calculated by these formulas:
·
Curtate life expectancy 
is the same as an
“immediate” life annuity with annual payments at the end of the year, and 𝑖 = 0.
·
Complete life expectancy 
is curtate life
expectancy plus 1/2 year.
· Joint life expectancy is the expected future lifetime for two persons aged 𝑥 and 𝑦, based on the probability of survival of both 𝑥 and 𝑦 from the current age to each future age. The joint life status ends upon the first death.
Complete joint life expectancy 
is calculated by the following formula:
· Last survivor life expectancy is the expected future lifetime for two persons aged 𝑥 and 𝑦, based on the probability of survival of either 𝑥 or 𝑦 from the current age to each future age. The last survivor status ends upon the second death.
Last survivor complete life expectancy 
is calculated by the following formula:
Thus, we have the following:
Excel functions
Click here
to see the various Excel functions to handle life expectancy and survival
functions.