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 A N N U The value of a direft prefentation is the fame as that of any other annuity for life, and is found for i 1. by the the table : which being multiplied by the yearly income, gives the value fought. .Prob. 5. To find the value of a reverfion for ever, after two fucceflive lives; or to find the value of a living after'the death of the prefent incumbent and his fucceflbr. Rule. By Prob. 3. find the value of the longeft of the two lives, and fubtraiS that value from the value of the perpetuity, and the remainder will be the value fought. Examp. A, aged jo, enjoys an eftate or living of 100 1. per annum-, B, aged 30, is intitled to his lifetime of the fame eftate after A’s death ; and it is propofed to fell the eftate juft now with the burden of A and B’s lives on it: What is the reverfion worth, reckoning intereft at ,4 per cent. ? By the table, A's life of jots, - - 11.34 B’s life of 30 is, 14.68 Sum, 26.02 8.60 Value of their joint lives, found by, Prob. 2. Cafe 2. js. i7.42fub. Value of the longeft life. 25.00 From the value of the perpetuity. Remains the value of 1 1. reverfion, 7.59-Multiply by 100 r* 758.00 Value of the reverfion, Prob. 6.. To find the value of the joint continuance of three lives, one life failing, the annuity to ceafe. Rule. Find the fingle values of the three live& from the table; multiply thefe fingle values continually, calling the refult the produift of the three lives; multiply that product by the intejeft of 1 1. and that produdl again by 2, calling the refult the double product; then, from the fum of the feveral products of the lives, taken two and two, fubtrad the double produd ; divide the produdl of the three lives by the remainder, and the quot will be the value of the three joint lives. Examp. A is 18 years of age, B 34, and C 56: What is the value of their joint lives, reckoning intereft at 4 per cent. ? < By the table, the value of A’a dife is 16.1, of B’s 1-4.12, and of C’s 10.01.

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T I E S. 16.1 X 14.12 X 10.01 = 2275.6, produft of the 3 lives. £4 91.024 _ 2 182.048, double produ<ft. • Produ'fl of A and B, 16.1 X 14.12 = 227.33 A and C, 16.1 X 10.01 = 161.16 B and C, 14112X10.01 = 141.34 Sum of all, two and two, 529.83 Double produd fubtraft - - 182.048 Remainder 347.782 And 347.782)2275.600(6.54 value fought. Prob. 7. To find the value of an annuity upon the longeft of three lives. Rule. From the fum-of the values of the three fingle lives taken from the table, fubtraft the fum of all the joint lives, taken two and two, as found by Prob. 2. and to the remainder add the, value of the three joint lives, as found by Prob. 6. and that fum, will be the value of the longeft life fought. Examp. A is 18 years of age, B 34, and C 56: What is the value of the longeft of thefe three lives, intereft at 4 per cent. ? By the table, the fingle value of A’s life is, 16.1 fingle value of B’s fife is, 14.12 fingle value of C’s life is, 10.01 Sum of the fingle values, 40.23 By Prob. 2. the joint vSlue of A and B is, 10.76 joint value of A and C is, 8.19 joint, value of B and C is, 7.65 Sum of the joint lives, 26^60^ Remainder, - - 13.63 By Prob. 6. the value of the 3 joint lives is, 6.54 Value of the longeft of the 3 lives, - 20.17 Other problems might be added, but thefe adduced' are fufficient for moft purpofes. The reader probably may wifti that the reafon of the rules, which, it muft be owned, are intricate, had been affigned; but this could not be done without entering deeper into the fubjedt than was pra&icable in this place. See Chance s.

ANN A NN ANNUITY of tiinds, in Scots law, a certain proporAnnulet is alfo a narrow flat moulding, which is tion of the tiends of erecfted benefices formerly payable common to divers places of the columns, as in the bato the crown, but now gone into difufe. fes, capitals, tec. It is the fame member which ViANNULAR, in a general fenfe, fomething in the form truvius calls a///?/; Palladio, a ItjieL or cincture; of, or refembling a ring. It is-alfo a peculiandeno'- Scamozzi, and Mr Brown, a fupercilium, HJl, tinea, mination for the fourth finger, commonly called the eye-brow, fquare, and rabbit. See Architecring-finger. ture. ANNULATA, in zoology, an obfolete name of a fpe- Anjjulet, inheraldry, a mark of diftindlion which the cies of coluber. See Coluber. fifth ANNULET, in archite&ure, a fmall fquare member in arms.brother of a family ought to bear to his coat of the Doric capital, under the quarter-round. The hieroglyphic of the annulet is very various; 1 Some.