3 tinuing n years, it will be worth a +(?} )a + (34)3a + (??)3a + (}} ) *a . . . . + (37) "a, which CHAP. IV. COMPOUND INTEREST AND ANNUITY TABLES. α As the architect is often called on to value property, we here add some practical obser vations on the subject, and a set of Tables for the ready calculation of such matters, which we shall at once explain. TABLE FIRST Contains the amount of 17. put out to accumulate at compound interest for any number of years up to 100, at the several rates of 3, 4, 5, 6, 7, and 8 per cent. The amount of any other sum is found by multiplying the amount of 17. found in the table at the given rate per cent., and for the given time, by the proposed sum. Example:-Required the amount of 755l. in 51 years, at 5 per cent. Amount of 11. for 51 years. at 5 per cent. is Given sum or 9090/. 158. 7d. 12-040769 755 £9080 780595 PAD IV. TABLE SECOND contains the present value of 17. 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 17. for the given number of years, at the proposed rate per cent., by the given sum or principal. COMPOL An annuity of 40%, is to commence 20 present value, the rate of interest beir Under 4 per cent, and opposite to 2 Under 4 per cent, and opposite to 50 Example: - Required the present value of 90902 payable 51 years hence, compound interest being allowed at 5 per cent. By the table, the present value of 14 payable at the expiration of 51 years at 5 per cent. is Given principal or 7541. 18s. 7 d. *083051 9090 £754-933590 Diference ::: 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. TABLE FOURTH shows the present value of an annuity of 17. 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. (This table provides for the percentage and to get back the principal.) Example:-Required the present value of an annuity of 451., which is to continue 48 years, at the rate of 5 per cent. Under 5 and opposite to 48 years is (years' purchase) or 8131. 9s. 5. 18.077157 45 £813-472065 Value To find the value of an annuity of twe g to the given ages, and at the pr product will be the required value. 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. That is the value of an annuity of 60L years, interest at 4 per cent.? E The number answering to 30 and 40 Annuity Value To fad the value of an annuity for the mediately preceding, but using E What is the value of an annuity of 60L. her 40 years, interest at 4 per cent. The tabular number answering at 4 Amanity Present value e first five tables which follow are p a simpson. The calculations involving the valuation ed on the architect, but it is absolutely the ease of valuations of leases upor Example. An annuity of 407, is to commence 20 years hence, and is to continue 30 years; required its present value, the rate of interest being 4 per cent. 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 500%. purchase, the rate of interest being 5 per cent.? Under 5 and opposite to 10 is Principal given •129504 500 or 641. 15s. Od. £64.752000 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 17. for 40 years at 4 per cent. is- Value 11.5 50 £575 To find the value of an annuity of 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 • Value 60 £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 604. 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 The first five 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 FIRST TABLE OF COMPOUND INTEREST. The Amount of One Pound in any Number of Years, &c. 1.045335 1.060596 1.075929 1.091336 1·106816 1.122368 9-156391 2.772469 1.060900 1.081600 1·102500 1.123600 1.144900 1.166400 22-188701 3.555 2-827375 3647 1.076695 1-103019 9-291289 1 2-883368 9-254362 3739 2-940470 3-825 9-287997 1.125508 1.169858 1.215506 1.262476 1.310796 1360488 22-321992 1.142266 1.193026 1.245523 1.299799 1.159274 1-216652 1.276281 1.338225 1.355897 1.413861 $ 2356565 $-058089 4016 8.118651 $591652 4-116 3-180412 2-427262 4-217 S-243597 4-321 9-463402 1.211830 1.290377 1.373189 1.460454 1.552367 1-649128 2:500080 9-575082 25573043-439934 3-373133 4:53 4-650 9613423 8-508058 3.577532 4.761 4.882 2-6918263-7206835126 3-648381 500 10 1-343916 1.480244 1-628894 1.790847 1.967151 2.158925 9772581 3.794316 2813862 3-869458 5-253 8.946088 5-383 5-516 2-104851 2.331639 2-855758 2.423110 9498278 4024236 2-252191 2.518170 9-941431 4-103932 5-632 9045926 4.185206 5-791 3029674 4-268089 5-93 4.352614 6.04 6-231 4-488813 141 1.535110 1.765970 2-028826 2-327743 2-667256 3.052421 3-167026 4-526719 6.38 15 1.557967 1-800943 2.078928 2.396558 2.759031 3.172169 3-214181 4-616365 6.54 3-262037 4-707788 670 4-801020 6.870 3.425942 3-310606 7039 3550898 4-896099 8-409924 4-993061 7-219 3460695 5-091943 7-397 3:512222 5-192783 7-57 5.295621 7-767 2.938722 3.496229 4.152785 3:564516 7-95 8-617589 5-400495 3671432 5.507446 8-14 4.660957 3726117 5-616515 8.33 3781595 5-727744 8.55 5-841175 8.76 3.399563 4.140562 5033833 3-837900 8.98 3-895043 5-956858 4.430401 5.436540 9-959037 6074822 9-20 4.582843 5.649818 4011895 4071628 6-195127 9.43 6-317815 9-66 3.932672 4.903642 6.101804 4132251 6.442933 6.341180 4193777 5.246897 6.589948 4-256219 6-570528 4-319590 6-700650 10.40 4-383906 6.833349 10 6 6.968676 10.97 7106683 11-1 11:4 T 48 481 49 4.132251 6.570528 10.401269 16.393871 25.728906 40.210573 4.193777 6.700650 10.658129 16.878524 26.614187 41.788053 4-256219 6.833349 10.921333 17.977504 27.529929 43.427418 491 4.319590 6.968676 11.191036 17.891235 28.477180 45.131097 50 4.383906 7.106683 11.467399 18.420154 29.457025 46.901612 |