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The Principles and Doctrine of Assurances: Annuities on Lives, and ...
No preview available - 2018
2ams ams 2amsr 2dly 3ams 3dly according added ages of A. B. amount annual annuity answer appears approximation assurance beginning Cent computed contingency COROLLARY correct death decease deducted demonstration denote depend derived determine died difference discounted divided dying equal EXAMPLE exists expectation expressed fails find the value former four given sum payable gives half happen Hence hypothesis increased by unity joint lives A. C. latter leaves less Let the ages lives aged longest manner multiplied nearly Note number of persons obtained older oldest operations payment perpetuity persons living preceding Prob probability PROBLEM quantities quotient rate of interest remainder respectively reversion rule Society SOLUTION subtracted Supposing surviving Table table of observations term third three joint lives three lives tion value required whole value younger youngest
Page 301 - To find the present value of a given amount to be received at the end. of any number of years not exceeding...
Page 51 - Simpson, for' finding the values of any three from the values given of any t r d& joint lives. " Let A be the youngest, and C the oldest " of the three proposed lives. Take the " value of the two joint lives B and C, and " find the age of a single life D of the same " value. Then find the value of the joint " lives A and D, which will be the
Page xii - every assurance made for the purpose of providing for a surviving family, in whatever office it is effected, not only as a private but as a public good.
Page 77 - the value of an annuity on the longest of two equal ' lives, whereof the common age is that of the older of ' the lives A and B; which value subtract from the ' perpetuity, and take half the remainder; then it will ' be, as the expectation of duration of the younger of ' the lives A and B, is to that of the older, so is the ' said half remainder to the number of years purchase ' required, when, the life of B is the older of the two.
Page 77 - ... lives, which value subtract from the perpetuity, and take half the remainder ; then say, as the expectation of duration of the younger of the two lives is to that of the older, so is the said half remainder to a fourth proportional ; which will be the number of years purchase required when the life of B in expectation is the older of the two ; but if B be the younger, then add the value so found to that of the joint lives A and B, and let the sum be subtracted from the perpetuity, which gives...
Page 131 - Jirsi or last that shall fail of the three lives A, B, and C. SOLUTION. If B be the oldest of the three lives, the value of the given sum will be S into r ~ XV-, ABC- r ~ . AF - AFC . AF- AFC . » I— " m APT _: A + AP + £ X r- iV- A;.
Page 81 - B ; which value fubtraft from the ?' perpetuity, and t-ake half the remainder ; then it will " be, as the expectation of duration of the younger of " the lives A and B, is to that of...
Page vii - ... lives of those improvident persons, who, in the " disposal of their property, seemed to have as " little consideration for their families as for them" selves; and as the price of an annuity on a life, " however young, very rarely exceeded seven years " purchase, the Assurances were seldom made for " a longer term, so that a very small proportion was " made on the whole continuance of life, or with any " other view than to secure a purchaser from the