Case 5. 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 701 per Annum (payable Yearly) amount to in 4 Years at 4 per Cent. per An num? (15) If a Salary of 100/ per Annum, to be paid Yearly, be forborne 6 Years, or unpaid, at 5 per Cent. per An num, what is the Amount ? (16) A Minor of 14 had an Annuity left him of 701 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 301 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. EXAMPLES. (18) What Pension, being forborne 6 Years, at 5 per Cent. will amount to 680/ 3s 94d.,6288 ? (19) What Annuity will amount to 5361 7s 52d.,45984 in 7 Years, at 3 per Cent.? (20) If the Payment of an Annuity, forborne for 30 Years, amount to 1548/ 13s 74d. at 34 per Cent. what is the Annuity? T 2 Case 7. When U, A, and R, are given, to find T. 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 100/ per Annum amount to 680/ 3s 94d at 5 per Cent.? (22) In what Time will an Annuity of 701 amount to 536/ 7s 14d,45984 at 3 per Cent.? (23) In what Time will 30 per Annum amount to 1548/ 13s 74d, 45984 at 3 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 17 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 100/ per Annum amount to 6861 3s 924d.,6288 in 6 Years? (25) At what Rate per Cent. per Annum will an Annuity of 701 per Annum amount to 5361 7s 54d.,45984 in 7 Years? (26) At what Rate per Cent. per Annum will a Salary of 30/ per Annum amount to 15487 13 74d.,0264 in 30 Years? LXIX. PRESENT WORTH of ANNUITIES, &c. THE 5th Table shows the present Worth of 1/ Annuity for any Number of Years under 31, at 3, 31, 4, 42, 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,90703÷1,05, 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, 34, 4, 44, 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 14. will purchase at the same Rate for the same Time. TABLE V. The present Worth of One Pound per Annum, or Annuity, for Years. Years. 3 per Ct. 3 per Ct. 4 per Ct.4 per Ct. 5 per Ct. 12 I 0.9708738 0.9661836 0-9615385 0.9569378 0.9523809 2 1.9124697 1.8996943 1.8860947 1.8726678 1.8594104 3 2.8286114 2.8616370 2.7750910 2.7489644 2.7232480 3.7170984 3.6730792 3.6298952 3.5875257 3.5459505 4.5797072 4.5150524 4.4518223 4-3899767 4.3294767 5.4171914 5.3285530 5.2421369 5.1578725 50756921 7-6.2302829 6.1145439 6.0020547 5.8927009 5.7863737 7.0196922 6.8739555 6.7327448 6.5958861 6.4632128 27.7861039 7.6076865 7.4353314 7.2687905 7.1078217 8.5302028 8.3169053 8.1108955, 7.9127182 7-7217349 II 9.5256241 9.0015510 8.7604763 8.3289169 8.3064142 9.9540040 9.6633343 9.3850733 9.1185808 8.8632516 13.10.6349553 10.3027585 9.9856473. 9.6828524 9.3935730 14 11.2960734 10.9205203 10.5631224 10.2228253 9.8986409 1511.9379351 11.5174109 11.1183868 10.7395457 10.3796380 16 12.5611020 12.0941168 11.6522949 11.2340151 10.8377695 17 13.1661885 12.6513206 12.1656680 11.7071914 11.2740622 1813-7535131 13.1896817;12.6592961 12.1599918 11.6895869 1914.3237991 13.7098374 13.1339385 12.5939936 12.0853208 20 14.8774748 14.2124033 13.5903253 13.0099365 12-4622103 21 15.4150241 14,6979742 14.0291589 13-4047239 12.8211527 22 15.9369166 15.1671248 14.4511142 13.7844248 13.1630026, 23 16.4436084 15.6204105 14.8568405 14.1477749 13.4885739 24 16.9355421 16.0583676 15.2469610 14.4954784 13.7986418 25 17.4131477 16.4815146 15.6220787 14.8220089 14.0939445 26:17.8768420 16.3903503 15.9827678 15.1466115 14.3751853 27 18.3270315 17.2853645 16.3295844 15.4513018 14.6430336 28 18.7641082 17.6670188 16.6630618 15.7428735 14.8981272 29 19.1884546 18.0357670 16.9837132 16.0218885 15.1410735 30 19.6004413 18.3920454|17.2920318 16.2888885 15.3724510 |
