## The Principles and Doctrine of Assurances: Annuities on Lives, and Contingent Reversions, Stated and Explained |

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### Contents

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### Other editions - View all

The Principles and Doctrine of Assurances: Annuities on Lives, and ... William Morgan No preview available - 2018 |

The Principles and Doctrine of Assurances, Annuities on Lives and Contingent ... William Morgan No preview available - 2015 |

### Common terms and phrases

2ams 2amsr 2dly 3ams 3dly 4thly ages of A. B. ampton ants assurance bability become extinct Cent compound interest computed contingency Corollary decease Decr deducted denote died Difference of Age divided by 1.03 dying equal age events:—1st ExAMPLE express the probability Find by Prob find the value fractions expressing given sum payable increased by unity joint lives A. B. C. joint lives A. C. joint lives aged Let the ages longest Moivre's hypothesis Northampton Table Note number living number of lives number of persons older oldest perpetuity persons living present value quotient rate of interest respectively reversion rule ScholIUM second that fails single and joint single lives solution subtract the value Supposing the ages surviving Table IV.-continued table of observations theorem third three joint lives tingency value required values of annuities whole value xxiii younger youngest

### Popular passages

Page 304 - What is the interest of $ 81, for 2 years 14 days, at ^ per cent. ? £• per cent. ? £ per cent. ? 2 per cent. ? 3 per cent. ? 4£ per cent. ? 5 per cent. ? 6 per cent. ? 7 per cent. ? 7£ per cent. ? 8 per cent.?

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 i - PRINCIPLES AND DOCTRINE OF ASSURANCES, ANNUITIES on LIVES, and CONTINGENT REVERSIONS, stated and explained. By W. MORGAN, FRS Actuary to the Society for Equitable Assurances on Lives, &c.

Page 51 - 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 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

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 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 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...