Page:Encyclopædia Britannica, first edition - Volume I, A-B.pdf/369

 A N N U I Rule. By the preceding problem, find the prefent worth of i h annuity for the rate and time given ; and then fay. As the prefent worth thus found toil, annuity, fo the prefent worth given to its annuity; that is, divide the given prefent worth by that of i I. annuity. Examp. What annuity, to continue 5 years, will 173!. 3 s. 7. purchafe, allowing compound interefi: at 5 per cent. .05 : 1 :: 1 : 201. 1.05 X 1.05 X 1.05 X i.oj X 1.05 = 1.2762815625 1.2762815625)20.000000000(15.6705. 20 15.6705 4.3295 prefent worth of 11. annuity. 4.329)173.179(40!. annuity. Anf. II. Annuities for ever, or freehold EJlates. In freehold ellates, commonly called annuities in feefimple, the things chiefly to be confidered are, 1. The annuity or .yearly rent. 2. The price or prefent worth. 3. The rate of intereft. The queftions that ufually occur on this head will fall under one or other of the following problems. Prob. 1. Annuity and rate of intereft given, to find the price. As the rate of 11. to 11. fo the rent to the price. Examp. The yearly rent of a fmall eftate is 40 1.: Whateris it worth in ready money, computing intereft at -34 P cent. L. s. d. As .035 : 1 40 : 1142.857142= 1142 17. ii Prob. 2. Price and rate of intereft given, to find the rent or annuity. As 11. to its rate, fo the price to the rent. Examp. A gentleman purchafes an eftate for 40001. and has 4^ per cent, for his money: Required the rent.. As 1 : .045 :: 4000 : i8ol. rent fought. Prob. 3'. Price and.rent given, to find the rate of, intereft. As the price to the rent, fo 1 to the rate.. Examp. An eftate of 180I. yearly rent is bought for 40001. : What rate of intereft has the purchafer for his money. ? As 4000 : 180 :: l : .045 rate fought. Pros. 4. The rate of intereft given, to find how. many years purchafe an eftate is worth. Divide 1 by the rate, and the quot is the number of years purchafe the eftate is worth. ] Examp. A gentleman is willing to purchafe an eftate, provided he can have 2-§- per cent.'Pox his .money: How many years purchafe may he offer ? .025)1.000(40 years purchafe. Anf, Prob. 5. The number of years purchafe at which an. eftate is bought or fold, given, to find the rate of intereft. Divide 1 by the number of years purchafe, and, the quot is the rate of intereft. Examp. A gentleman gives.40 years purchafe for an eftate: What intereft has he for his money ? 4p)i,ooo(.025 rate fought.

T I E S. 319 The computations hitherto are all performed by a fingle divifion or multiplication, and it will fcarcely be perceived that the operations are conduced by the rules of compound intereft ; but when a reverfion occurs, recourfe muft be had to tables of annuities on compound intereft. Prob. 6. The rate of intereft, and the rent of a freehold eftate in reverfion, given, to find the prefent worth or value of the reverfion. By Prob. 1. find the price or prefent worth of the eftate, as if pofTeflion was to commence prefently; and then, by the Tables, find the prefent value of the given annuity, or rent, for the years prior to' the commencement ; fubtradt this value from the former value, and the remainder is the value of the reverfion. Examp. A has the poffelfion of an eftate of 130I. per annum, to continue 20 years ; B has the reverfion of the fame eftate from that time for ever : What is the value, of the eftate, what the value of the 20 years pofleffion, and what the value of the reverfion, reckoning compound intereft at b per cent. By Prob. 1. .06)130.00(2166.^666 value of the eftate. By Tables 1491.0896val.ofthepoffeffion. 6 7 5.5 7 70 val. of the reverfion. Prob, 7. The price or value of a reverfion, the time prior to the commencement, and rate of intereft, given, to find the annuity or rent. By the Tables, find the amount of the price of the reverfioa for the years prior to the commencement; and then, by Prob. 2. find the annuity which that amount will purchafe. Examp. The reverfion of a freehold eftate, to commence 20 years hence, is bought for 675.57 71. compound intereft being allowed at b per cent.'. Required', the annuity or rent. By theTables the amount of 675.577 1- ? 2I^ a for 20 years, -ex bper cent, is j. By Prob. 2. 2166.6X .06= 130.0 rent fought.. III. Life Annuities. Th e value of annuities for life is determined from ob-; fervations made on the bills of mortality. Dr Halley, Mr Simpfon, and Monf. de Moivre, are gentlemen of. diftinguilhed merit in calculations of this kind. Dr Halley had recourfe to the bills of mortality at Breflaw,. the capital of Silefia, as a proper ftandard for the .©tiier parts of Europe, being a place pretty- central, at a diftance from the fea, and not much crowded with traffickers or foreigners-.. He pitches upon 1000 perfons all born in one year, and obferves- how many of thefe were alive every year, from their birth to- the extinftion of the laft,. and confequently how many died each year, as in the firft of the following tables; which is well? adapted to Europe in general. But in the city of London, there-is obferved to be a greater difparity in the births and burials than in any other place, owing probably to the vaft refort of people thither, in the way of commerce, from all parts of the known world. Mr Simpfon, therefore, ip order to have a table particularly.. faitedi