## The Doctrine of Annuities and Reversions, Deduced from General and Evident Principles: With Useful Tables, Showing the Values of Single and Joint Lives, &c., at Different Rates of Interest. To which is Added a Method of Investigating the Value of Annuities by Approximation, Without the Help of Tables. The Whole Explain'd in a Plain and Simple Manner and Illustrated by Great Variety of Examples |

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### Common terms and phrases

according added againſt annuity anſwering appear ariſing becauſe caſe cent chance combination conſidered continuing COROLLARY correſponding deceaſe depends determined difference divided equal eſtate EXAMPLE expectation expreſſes failing fame find the value firſt fore former given age gives greater half happen heirs Hence interval laid laſt latter leaſt leaves leſs longeſt manner Mean Age method multiply multiply'd nuity number of joint number of lives number of perſons obſervations paid perat perpetuity perſons poſſeſſion preceding preſent value Prob probability PROBLEM propoſed Purch quotient rate of intereſt reaſoning receive remain renewals reſerved reſpectively reverſion rule ſame ſecond ſhall ſince ſingle SOLUTION ſome ſubtract ſum ſuppoſed ſurviving taken theſe thoſe three joint lives three lives true value required Value Value Value whence whole year's purchaſe year's rent Year's Year's Year's yearly

### Popular passages

Page 112 - To find the present value of a given amount to be received at the end. of any number of years not exceeding...

Page 114 - The present value of an annuity of one pound for any number of years not exceeding 100.

Page 6 - ... only 93 of them arrive to the age of 66 : therefore, feeing the whole number of perfons living at the beginning of this term, is to the number remaining alive at the end of it, in the ratio of 331 to 93 ; the number of chances that a perfon of 36 years of age has to live 30 years longer, will be to the number of all the chances...

Page 2 - ... to the whole number of inhabitants ; and therefore the probabilities of life,, for all ages above 25 years, the fame as this author has made them ; but then have increafed the numbers of the living...

Page 2 - a place where the generality of the people live to a " greater age than at London (as appears by comparing the Bills " of Mortality here with those observations) can be no just " measure of the probability of Life in this place

Page 7 - ... 89.65, will be the true value of the fecond year's rent. And by a like way of proceeding, the values of the 3d, 4th, 5th, &c.

Page 128 - I apprehend could only be owing to a want of obfervations ; becaufe, if we fuppofe as many perfons to live, at any one time...

Page v - Lastly, arc laid down some easy practical rules for approximating the values of lives without the help of tables. What. I apprehend, may best recommend this performance, is the general, yet familiar manner in which the subject is treated : there not being a solution throughout the whole work, except those relating to the use of tables, that is not universal according to any table or obs. or degree of prob. of life whatsoever; and yet...

Page 7 - ... 96.15, in order to make a juft deduction out of it, for the contingency of his dying before the end of one year, ought to be...

Page 3 - Only, that are born within the bills. Which was done, by comparing together the number of chriftenings and burials, and obferving, by help of Dr.