The calculation of the values of joint lives front any given table of mortality, for every combination of age, is so labo rious a task, that no such table has yet been published. Mr. Simpson, in his se. lect exercises, gave a table of the values of two joint lives, agreeable to the proba bilities of life in London ; but the tables founded on the London bills, representing the rate of mortality among the inhabi tAnts, taken in the gross, give the values of lives much too low for the middling and superior classes of' the people in London itself, and are wholly improper for gene ral use. A much more comprehensive table of the value of joint lives has since been calculated by Dr. Price from the Northampton table of mortality, from which the following table is taken.
To find the value of any annuity dining the continuance of u life of any. given age, or during the joint continuance of two lives, it is only necessary to multiply the value in the table, against the given. age, by the annuity; or to find the annui ty equivalent to any certain sum,- divide the sum by the value in the table against the given age.
Exsortas.—What is the difference in value between an annuity of 50/. during the life of a person aget135, and an annui ty- of 60/. during two lives of 30 and 35,
to cease when either of the tu-o lives shall fail ? The valuta in Table 111. against the age of 35 is 12,502, which multiplied by 50 gives 625.1/. the value in table V. against the ages of 30 and 35 is 9.954, which mul tiplied by 60 gives 597.24/. the value of the former. annuity therefore exceeds the lattet by 27k17s. 2d.
WTiat annuity during his life, ought a person aged 45 to receive in lieu of an annuity of 20/. certain for the term of 18 years ? The value of an annuity certain for 18 years, is by Table II. 11.689587, which multiplied by 20 gives 233.7917/. this sum divided by 11.105, the value of an annuity during a life bf 45, by Table 111. gives the answer of 21/. ls.
What annuity during his life, ought a person aged 40 to receive for 500/.
The value of an annuity during a life of 40 years of age, is by Table 11.837, and 500/. divided by this sum gives 42/. 4s. 911 per annum ; but if the value of the life is taken, as in Table IV. (or 13.466), the stlin to be received will be 37/. 2s. 7d.
For the values of anmtities which are not to coinmence till after a certain peri od, or after a given life or lives. See RE.