TABLEs SixTH, SeveNTH, and EIGHTH are for finding the value of annuities on single and joint lives, and were constructed by Simpson, on the London bills of mortality. To find the value of an annuity for a single life, at a proposed rate of interest, within the limits of the table, take from Table VI. the number answering to the given age and proposed rate of interest, which multiplied by the given annuity, the product will be the value required. Example. What is the value of an annuity of 50l. upon a single life aged 40 years, according to the London bills of mortality, the rate of interest being 4 per cent.? The value of an annuity of 11. for 40 years at 4 per cent. is - - - 11-5 Annuity - - - - - - - - - - - 50 Value - - - - - - - - - - - £575 To find the value of an annuity for two joint lives, multiply the number in Table VII. answering to the given ages, and at the proposed rate of interest, by the given annuity, and the product will be the required value. Example. What is the value of an annuity of 60l for two joint lives, the one being 30 and the other 40 years, interest at 4 per cent. ? The number answering to 30 and 40 years at 4 per cent. is - - - 8-8 Annuity - - - - - - - - - - - - 60 Value - - - - - - - - - - £528.0 To find the value of an annuity for the longest of two given lives, proceed as directed in the case immediately preceding, but using Table VIII., and the product will be the value. Example. What is the value of an annuity of 60l. for the longest of two lives, the one being 30 and the other 40 years, interest at 4 per cent.? The tabular number answering at 4 per cent, is - - - - 15-9 Annuity - - - - - - - - - - - 60 Present value - - - - - - • - - - £954-0 The five first tables which follow are printed from those of Smart; the remainder are from Simpson. The calculations involving the valuation of annuities on lives are not very frequently imposed on the architect, but it is absolutely necessary he should be capable of performing them, as in the case of valuations of leases upon lives, which sometimes occur to him. The public think that the actuaries of life offices in such cases are the only persons capable of affording information on those subjects; but if they knew as much as we do of the absolute want of mathematical knowledge of seven eighths of these attachés, they would pause before consulting them. There are some few, however, of this class, who in point of knowledge of the subject in question dignify the offices they hold, among whom none can be placed in every attainment of the highest rank superior to Mr. Galloway, the present actuary of the Amicable office. It cannot be supposed that this observation is made from jealousy of the parties, inasmuch as their pursuits are so widely different from those which we follow, that clashing with them would be next to an impossibility. THE FIRsr TABLE of CoMroUND INTEREst. The Amount of One Pound in any Number of Years, &c. F-T—- –– —I-, |Years. 3 per Cent. 4 per Cent. 5 per Cent. 6 per Cent. 7 oer Cent. 8 per Cent. 13 1-468533 1-665073 | 1.885649 2-132928 || 2:409845 2.719623 13| | 1.490.398 || 1 698048 || 1:932215 || 2:195984 || 2:492763 2-82631.5 14 1.5.12589 | 1.731676 | 1.9799.31 || 2:260903 || 2:578534 2.937193 14, 1:535110 | 1.76597o || 2:02.8826 || 2:327743 2.667256 || 3:052421 15 1.557967 1-800943 || 2:078928 || 2:396558 2.759031 || 3-1721.69 153 1-581 164 1-836.609 2-130267 2.467.407 2-853964 3.29.6614 16 1:604706 1-872.981 2-18287.4 2'540351 2-952,163 3.425.942 16} 1-628599 1.91OO73 2-236780 2-615452 3-053741 3-56.0344 17 1.652847 1 947,900 2.292018 2.692772 3-1 58815 3.700018 17; 1-67.7457 1 '986476 2-348.619 2-772379 3-267,503 3-84.5171 l‘702433 2-025816 2-4O6619 2-854339 3.37.9932 3.996019 181 | 1.727780 2-065935 2:466.050 2.9387.22 3.496.229 4*152785 19 1-75.3506 2-106849 2-5269.50 3.0255.99 3-616527 4-3.15701 191 | 1.779614 2-148573 2°589353 3-115045 3-740965 4-485008 2O 1-806111 2-191123 2.653.297 3.207135 3.869684 4'660957 20] 1-8330O2 2-23451.5 2.718821 3'301948 4-002832 4.84.3808 21 1 *860294 2.278768 2.785962 3-399.563 4-140562 5.033833 211 1-887992 2-323896 2.854762 3-500064 4:28:3031 5.231.313 22 1-916,103 2-3699.18 2.92.5260 3.603537 4-43O401 5-436540 22} 1 9446.32 2-416852 2.997:500 3-71.0068 4-58284.3 5-6498.18 23 1 -97.3586 2.464715 3.071,523 3.819749 4:740529 5-87.1463 23] 2.002971 2.513.526 3-147375 3.932672 4-903642 6-101804 24 2-032794 2-563304 3.22.5099 4'048934 5:07:2366 6-341180 24! 2:06:3060 2-614067 3.304744 4-168633 5.246897 6:589948 25 2-0937.77 2-66.5836 3.3863.54 4-291870 5.427.432 6.848475 |