TABLE Second contains the present value of 11. payable at the end of any number of years up to 100. The present value of any given sum payable at the expiration of any number of years is found by multiplying the present value of 11. for the given number of years, at the proposed rate per cent., by the given sum or principal. Example. Required the present value of 9090l payable 51 years hence, compound interest being allowed at 5 per cent. By the table, the present value of 11 payable at the expiration of 51 years at 5 per cent. is - - - - - - - ‘O83051 Given principal - - - - - - - - - 9080 f 754-923590 or 754l. 18s. 5;1. TABLE THIRD contains the amount of an annuity of 11. for any number of years, and is thus used. Take out the amount of 11. answering to the given time and rate of interest: this multiplied by the given annuity will be the required amount. Example. Required the amount of an annuity of 271 in 21 years, at 5 per cent. compound interest. Annuity of 11 in 21 years at 5 per cent. - - - - - 35-7 19251 TABLE Fourth shows the present value of an annuity of 11 for any number of years, at 3, 4, 5, 6, 7, and 8 per cent., and is used as follows : — First, when the annuity commences immediately. Multiply the tabular number answering to the given years and rate of interest by the given annuity, and the product will be the value required. Example. Required the present value of an annuity of 45l., which is to continue 48 years, at the rate of 5 per cent. Under 5 and opposite to 48 years is (years' purchase) - - 18.0771.57 Second, when the annuity does not commence till after a certain number of years. Multiply the difference between the tabular numbers answering to the time of commencement and end, at the proposed rate of interest, by the given annuity, the product will be the present value required. Example. ... An annuity of 40l. is to commence 20 years hence, and is to continue 30 years; required its present value, the rate of interest being 4 per cent. Under 4 per cent. and opposite to 20 is - - - - - 13.590.526 Under 4 per cent. and opposite to 50 (20+30) is - - - 2l 482184 Difference - - - - - - - - - - 7 '891858 Annuity given - - - - - - - - - 40 Table Fifth contains the annuity which 11, will purchase, compound interest being allowed. The manner of using this table is obvious, from what has been said relative to the preceding tables. Example. What annuity for 10 years will 500l. purchase, the rate of interest being 5 per cent.” Under 5 and opposite to 10 is - - - - - - •l 29.504 Principal given - - - - - - - - - 500 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. 2 The value of an annuity of 11. for 40 years at 4 per cent. is - - - ll '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. 2 The number answering to 30 and 40 years at 4 per cent. is - - - 8-8 Annuity - - - - - - - - - - - - 60 Value - - - - - - - - - - £528 O 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 so 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-O 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. o THE FIRsr TABLE or Compound INTEREst. |- The Amount of One Pound in any Number of Years, &c. | |- Years. 3 per Cent. 4 per Cent. 5 per Cent. 6 per Cent. 7 ner Cent. 8 per Cent. ! 1 or 4889 1-019803 1-024.695 1-029563 1-034408 1-039230 |- I 1-030000 1-0.40000 1-050000 1-060000 1-070000 1-080000 14 1-045335 1-060,596 1-075929 1-091336 1-106816 1-122368 2 1-060900 1-081600 1-102,500 1-12:3600 1-144900 1-166400 2. 1-076695 1-103019 1-1297.26 1-156817 1-184293 1-212,158 3 1-092727 1-124864 1-157625 1-191016 1-225043 1-259.712 3. 1-108996 1-147140 1-186212 1-226226 1-267,194 1-8091.31 o 4. 1-125508 1-169858 1-215506 1-262476 1-3107.96 1 360488 44 1-142266 1-1930.26 1-24.5523 1-299799 1-355897 1-413861 1-1592.74 1-216652 1.276281 1-3382.25 1 402551 1-469328 I 5. ! 18 1-702433 2-025816 2-4.06619 2-854939 3-379932 3.996019 18. 1-72.7780 2-065935 2-466.050 2-9387.22 3-49.6229 4-152785 19 1-753506 2-106849 2-5269.50 3-0255.99 3-6165.27 4-3.15701 19. 1-7796.14 2-148573 2-589853 3-115045 3-740965 4-485008 20 1-806111 2-191123 2-653.297 3-207135 3-869684 4-660957 20] 1-8330.02 2-234,515 2-718821 3-301948 4-oo.2832 4'848808 21 1-860294 2-278,768 2-78.59.62 3-399.563 4-140562 5-033833 21] I-88.7992 2-328896 2-854762 3-500064 4-28.3031 5-231.313 22 I-916,103 2-369.918 2-9.25260 3-603537 4-430401 5-436,540 22, I-94.4632 2-416852 2-997.500 3-71.0068 4-58284.3 5-6498.18 23 I-973,586 2-464715 3-07-1523 3-819749 4-7.40529 5-87.1463 23. 2-002.971 2-513,526 3-1473.75 3-932672 4-903642 6-101804 24 2-0327.94 2-563304 3-225099 4-048934 5-072366 6-341180 24! 2-063060 2-6-14067 3-3o4744 4°1686.33 5-246897 6-589948 25 2-09:37.77 2-665836 3-3863.54 4-291870 5-427.432 6-848475 |