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36 HASKINS & SELLS May THE accountant sometimes is confronted with problems concerning compound interest, annuities, sinking fund contributions, and the like. He may be asked to find the present value of a lease calling for a certain number of periodic payments, or he may want to know what amount should be set aside each year to liquidate a debt at some future date. These situations arise frequently enough so that some knowledge of the mathematics of compound interest is considered an essential part of the technical equipment of the accountant. Tables have been published which facilitate the computations in the solution of compound interest problems. These tables are very helpful when accessible and almost indispensable in the more complicated instances. However, the accountant should be sufficiently familiar with the relationships of the several compound interest functions, so that he can solve elementary problems when published tables are not available or when the tables at hand are incomplete. One should, if necessary, be able to handle a fair proportion of investment problems through reasoning rather than through memorizing complicated formulas and the attendant algebraic symbols. There are six fundamental compound interest functions as follows: 1. Amount of $1 at compound interest. One dollar invested now at compound interest will amount to how much at the end of a certain period of time? 2. Present value of $1 at compound interest. What sum of money invested now at compound interest will amount to $1 at the end of a certain period of time? 3. Amount of $1 per period at compound interest. A periodic payment of $1 will amount to how much at compound interest at the expiration of a certain period of time? 4. Present value of $1 per period at compound interest. What sum of money invested now at compound interest would be just sufficient to make a periodic payment of $1 for a certain length of time? 5. Annuity which will amount to $1 at compound interest. What sum of money should be regularly set aside at compound interest to amount to $1 at the end of a certain period of time? 6. Annuity which has a present value at compound interest of $1. One dollar set aside now at compound interest will be just sufficient to make a regular payment of how much for a certain length of time? Computations are made on the basis of $1 because each dollar in a given transaction increases in the same proportion as every other dollar. The result then is multiplied by the number of dollars involved. Generally the dollar sign is omitted because the tables or computations may be considered as representing one unit of any monetary standard—the dollar, the pound, the franc, and so forth. Time usually is referred to by periods rather than by years, a period being the interval between two successive interest conversion dates. Interest rates also are adjusted to the basis of a period. The amount of 35,000 for three years at 4% per annum compounded quarterly would be considered, for purposes of computation, as the amount of $1 for 12 periods at 1% per period and the result multiplied by 5,000. 1. Amount of 1 The amount of 1 invested for one period at 4% is 1 x 1.04, or 1.04. The amount of 1 invested for two periods at 4% is equivalent to the amount of 1.04 invested for one period at 4% which is 1.04 x 1.04, or 1.0816. The amount of 1.0816 invested for one period at 4% is 1.0816 x 1.04, or 1.124864, which is the same as the amount of 1 invested for three periods at 4%, (1 x 1.04 x 1.04 x 1.04 = 1.124864). The ratio of the investment value at the end of a period to the value at the beginning of the period is known as the ratio of increase. The ratio Mathematics of Investments
Object Description
Title 
Mathematics of investments 
Author 
Anonymous 
Subject 
Annuities  Accounting Compound interest 
Citation 
Haskins & Sells Bulletin, Vol. 10, no. 05 (1927 May), p. 3640 
DateIssued  1927 
Source  Originally published by: Haskins & Sells 
Type  Text 
Collection  Deloitte Digital Collection 
Digital Publisher  University of Mississippi Libraries. Accounting Collection 
DateDigitally Created  2009 
Identifier  HS Bulletin 10p36 