Page:Encyclopædia Britannica, first edition - Volume I, A-B.pdf/372

 322 A N N U I T I E S. of one pound for an age of 50 years, at 3 per cent, inby the remainder, and the quot will be the value tereft, is 12.51 ; that is, 12 1. 10 s. or twelve and a ofprodudt 1 1. annuity, or the number of years purchafe fought. half years purchafe. The marginal figures on the left of Examp. What is the value of 70 1. annuity for the the column of age ferve to fhorten the table, and fignify, joint lives of two perfons, wherof one is 40 and the other that the value of an annuity for the age denoted by them, 50 years of age, reckoning intereft at 5 per cent. '? . is the fame with the value of an annuity for the age de- Bjr'the table the value of 40 years is, - 11.83 noted by the numbers before which they ftand. Thus And the value of 50 years is, - - 10.35 the value of an annuity for the age of 9 and 10 years is the fame; and the value of an annuity for the age of 6 Firft produft, 122.4405 and 14, for the age of 3 and 24, 'be. is the fame. The Multiply by .05 lurcher ufe of the table will appear in the queftions and problems following. Second produft, 6.122025 Quest, i. A perfon of 50 years would purchafe an annuity for life of 200 1: What ready money ought he Sum of the two lives, 22.180000 to pay, reckoning inteteft at 44 per cent. ? Second produft deduft, 6.122025 L. By the table the value of 1 1. is 10.8 Remainder, 16.057975 Multiply by 200 And 16.057975)122.4405(7.62 value of x 1. annuity. 7° Value to be paid in ready money 2164.00 Anf. Quest. 2. A young merchant marries a widow lady 533.40 value fought. ef 40 years of age, with ft jointure of 300 1. a-year, and Pros. 3. To find the value of an annuity upon the wants to difpofe of the jointure for ready money: What < longeft of two lives ; that is, to continue fo Jong as eifum ought he to receive* reckoning intereft at 34 per ther of the perfons is in life. cent.? Rule. From the fum of the values of the Jingle lives, L. fubtraft the value of the joint lives, and the remainder By the table the value of 1 1. is. 13.98 .will be the value fought. 300 •* ' Examp. 'What is the value of an annuity of 1 I. upop the Jongeft of two lives, the one perfon being 30, and Value to be received in ready money 4194.00 Anf. the other 40 years of age, intereft at 4 per cent. ? Pros. 2. To find the value of an annuity for the By the table, 30 years is, - 14.68 joint continuance of two liyes, one life failing, the an40 years is, - 13.20 nuity to ceafe. Here there are two cafes, according as the ages of the Value of their joint lives, by Prob. 2.7 27.88 two perfons.are equal or unequal. Cafe 2. is, 3 9 62 1. If the two perfons be of the fame age, work by the following Value fought, 18.26 Rule. Take the value of any one of the lives from If the annuity be any other than 1 1. multiply the anthe table, multiply this value by the intereft of 1 1. for fwer found as above by the given annuity. a year, fubtraA the produft from 2, divide the forefaid If the two perfons be of equal age, find the value of value by the remainder, and the quot will be the value their joint lives by Cafe 1. of Prob. 2. of 1 1. annuity, or the number of years purebafe fought. Pros. 4. To find the value of the next prefentation Examp. What is the value of 100 1. annuity for the to a living. joint lives of two perfons, of the age of 30 years each, Rule. From the value of the fucceflbr’s life, fubreckoning intereft. at 4 per cent. ? traft the joint value of his and the incumbent’s life, and By the table, one life of 30 years is - 14.68 the remainder will be the value of i 1. annuity; which Multiply by - .04 multiplied by-the yearly income, will give the fum to be Subtract the product 5872 paid for the next prefentation. From - - 2.0000 Examp. A enjoys a living of 100 I. per annum, and B would purchafe the faid living for his life after A’s Remains 1,4128 death: The queftion is, What he ought to pay for it, And 1.4128714.68(10.39 value of 1 1. annuity. reckoning intereft at 5 per cent. A'bejng 60, and B 25 And 10.39 * 100= 1039 the value fought. years of age ? 2. If the two perfons are of different ages, work as L. direfied in the. following By the table, B’s life is, - 13.46 Rule. Take the values of the two lives from the Joint value of both lives, by Prob. 2.. is, 6.97 table, multiply them into one another, calling the refult 6.49 the firft produdl; then multiply the faid firft product by The value of 1 1. annuity, the intereft of 1 1. for a year, calling the refult the feMultiply by - - 100 cond produdt; add the values of the two lives, and from their fum fubtratt the fecond produftj divide the firft Value of next prefsntation, - - - 649.00 The