Case 3. When U, T, and R are given, to find A... By Table III. thus: Multiply the annuity by the tabular number for the given time and rate, and the product will be the amount required. EXAMPLES. (14) What will an annuity of 70l. per annum (payable yearly) amount to in 4 years, at 4 per cent. per annum? 1 (15) If a salary of 100l. per annum, to be paid yearly, be forborne 6 years, or unpaid, at 5 per cent. per annum, what is the amount? (16) A minor of 14 had an annuity left him of 70%. a-year, the proceed of which, by will, was to be put out, both principal and interest, yearly, as it fell due, at 3 per cent. till he should attain to 21 years of age; the utmost improvement being made of this part of his fortune, what had he then to receive? (17) If an annuity of 30l. per annum, payable yearly, be omitted to be paid for 30 years, at 3 per cent. what is 'the amount? ; Case 6. When A, T, and R are given, to find U.; By Table III. thus; Divide the amount given by the tabular number for the given time and rate, and the quotient will be the annuity required, 121 1 EXAMPLES. (18) What pension, being forborne 6 years, at 5 per cent. will amount to 680l. 3s. 94d.,6288? (19) What annuity will amount to 536l. 7s. 54d.,45984 in 7 years, at 3 per cent.? (20) If the payment of an annuity, forborne for 30 years, amount to 15481. 13s. 7‡d. at 34 per cent. what is the annuity? Case 7. When U, A, and R are given, to find T. ́artu-a THEOREM 7. Rt. u Which proceed with as in Theorem the 3d, which will give T, the time. By Table III. thus: Divide the amount by the annuity, and the quotient will be the amount of 17. at the given rate, which will be found under the said rate even with the time required. EXAMPLES. (21) In what time will a salary of 100l. per annum amount to 6801. 3s. 94d. at 5 per cent.? (22) In what time will an annuity of 70l. amount to 5361. 7s. d.,45984 at 3 per cent.? (23) In what time will 30l. per annum amount to 15487. 13s. 7 d.,45984 at 34 per cent.? Case 8. When A, U, and T are given, to find R. This being a very high equation, it requires the assistance of Algebra to determine R by the Theorem. By Table III. thus: Proceed as in the last Rule, which will give the annuity that 11. will purchase for the given time, which will stand even with the said time, and under the rate required. EXAMPLES. (24) At what rate per cent. per annum would a salary of 1007. per annum amount to 6861. 3s. 94d.,6288 in 6 years? (25) At what rate per cent, per annum will an annuity of 70l. per annum amount to 5361. 7s. 54d.,45984 in 7 years? (26) At what rate per cent. per annum will a salary of 301. per annum amount to 15481. 13s. 74d.,0264 in 30 years? LXIX. PRESENT WORTH of ANNUITIES, &c. THE 5th Table shows the present worth of 17. annuity for any number of years under 31, at 3, 31, 4, 41, and 5 per cent. and is made thus: divide 1 by 1,05=,95238, the present worth for the first year, which 1,05,90703 added to the first year's present worth, 1,85941, the second year's present worth: again ,907031,05, and the quotient added to 1,85948=2,72324 third year's present worth, at 5 per cent., &c. ་ The 6th Table shows the annuity which 17. will purchase for any number of years under 31, at 3, 32, 4, 41, and 5 per cent. and is constructed by finding the present worth of 17. per annum in the fifth Table, at the assigned rate and time: and dividing unity or 1 thereby, the quotient will be the annuity that 17. will purchase at the same rate for the same time. 1 The present Worth of One Pound per Annum, or Annuity, for Years. Years. 3 per Cent. 3 per Cent. 4 per Cent. 4 per Cent 5 per Cent. 10,9708738 0,9661836 0,9615385 0,9569378 0,9523809 7,0196922 6,8739555 6,7327448 6,5958861 6,4632128 TABLE VI. The Annuity which One Pound will purchase for any Number of Years. Years. 3 per Cent. 3 per Cent. 4 per Cent. per Cent. 5 per Cent. 1,0300000 1,0350000 1,0400000 1,0450000 1,0500000 2,5226108 ,5264005 ,5301961 ,5339976 ,5378049 3,3535304 ,3569342,3603485 ,3637734 4,2690271 ,2722511 ,2754901 5,2183546 ,2214814 ,2246271 6,1845775 ,1876682 ,1907619 ,1938784 ,1970175 ,3672086 ,2785437 ,2820118 ,2277916 ,2309748 ,1016240 ,0931133 ,0963423 ,0890154,0922699 ,0854176,0886991 ,0855462 14,0885263 ,0915707 ,0946690 ,0978203 22 0527474,0659321 24,0590474,0622728 ,0735818 ,0822369 ,0794073 ,0827450 ,0768761 ,0802426 0712801 ,0746006 ,0779961 23,0608139 ,0640188 ,0673091 ,0706825 ,0741368 ,0655868 ,0689870 ,0724709 25,0574279 ,0606740 ,0640120 ,0674890 ,0709525 26,0559383 ,0592054 ,0625674 ,0660210 ,0695643 127,0545642 ,0578524 ,0612385 ,0647195 ,0683919 28,0532932 ,0566029 ,0600130 ,0635208 ,0671225 29,0521147 ,0554454 ,0588799 ,0624146 ,0660455 [30,0510193 ,0543713 ,0578301 ,0618903 ,0650614 |