APPENDIX IV. TABLES OF COMPOUND INTEREST AND DISCOUNT. Table I. The Summarised Future Value of a Capital (C) of 1, accumulating at Compound Interest for n years, the rate of Interest being p. Cn=C × 1·0p". II. The Discounted Present Value of a Capital (Cn) of 1, to be realised n years hence, the rate of Interest being p. III. The Discounted Present Value (C) of a Perpetual Periodic Rental or Return (R) of 1, obtainable every n years, the rate of Interest being p. IV.—The Summarised Future Value (Cn) of an Annual Rental or Return (7) of 1, obtainable for n years in all, the rate of Interest being p. C'n = "(1·0p" − 1) V. The Discounted Present Value (C) of an Annual Rental or Return (r) of 1, obtainable for n years in all, the rate of Interest being p. Examples of the Use of the Tables : Table I.—A capital of 1 at 3 per cent in 20 years becomes 1·8061; therefore £100 would become 100 x 1.8061180.61 £180, 12s. 2d. II.—A capital of 1 obtainable in 40 years has, at 3 per cent, a present value of only 0-3066; therefore £100 would only have a present value of 100 × 0·3066 =30.66 £30, 138. 2d. III.-A return of 1 due 10 years hence, and every 10 years after that, has at 4 per cent a present value of 2.0823; therefore a similar return of £20 (as, for example, the net income from a piece of coppice cut every 10 years) would have a present value of 20 × 2·0823=41·646 = £41, 12s. 11d. IV.-A return of 1 obtainable for the next 20 years represents, at 3 per cent interest, 26-8704 at the end of that time; therefore a hunt leasing a piece of woodland as a fox-covert for 20 years at a rental of £20 a year, will by the end of that time have paid a sum equal to 20 × 26·8704=537·408 = £537, 8s. 2d. Note. And conversely, this table can be used to ascertain the annual payment necessary to establish a Fund which will amount to a certain sum in n years, through dividing the capital by the final value C (r=1-0 pm - 1 For example, if £5000 are payable 20 years hence, what sum must be invested annually at 3 per cent to form a fund that will clear the debt then? Here r 5000÷ 26.8704186-07 £186, 18. 5d. V. An annual return of 1 obtainable for the next 20 years has, at 3 per cent interest, a present value of 14.8775; therefore a rental of £20 a year payable by a hunt leasing a wood for 20 years as a fox-covert would, at 3 per cent, be equal to a present total payment of 20 × 14.8775=297.55=£297, 118. Note.-And conversely, the annual sum required to liquidate within the course of n years a debt now incurred, is ascertained through dividing this sum by the present value as shown in this table (r=Cx 10 p" x 0.0p 1-0 pm-1). For example, if a debt of £5000 be now incurred, it can, reckoning 3 per cent interest, be gradually liquidated (along with the interest due on it) in 20 years by an annual payment of r = 5000 ÷ 14.8775=336·077=£336, 1s. 6d. accumulating at Compound Interest for n years, the rate of Interest being p. 150 19.4996 40.6050 84.2527 174.2017 2760.147 358.9227 736.9594 1507.978 531.2932 1144-475 2456-336 4001·113 6517.392 1777.335 4286 425 10616.14 6656 686 17292.58 VOL. II. 2 D TABLE II.—THE DISCOUNTED PRESENT VALUE OF A CAPITAL (C) of 1, to be realised n years hence, the rate of Interest being p. PERIODIC RENTAL OR RETURN (R) of 1, obtainable every n years, the rate of Interest being p. 12345 50-0000 40.0000 33.3333 28.5714 25.0000 22.2222 20.0000 9.1981 8.0087 6.7786 5.8873 5.3280 4.6157 4.0620 3.6195 |