Merton-Chpt2 - II. ON THE ARITHMETIC OF COMPOUND INTEREST:...

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8 II. ON THE ARITHMETIC OF COMPOUND INTEREST: THE TIME VALUE OF MONEY From our everyday experiences, we all recognize that we would not be indifferent to a choice between a dollar to be paid to us at some future date (e.g., three years from now) or a dollar paid to us today. Indeed, all of us would prefer to receive the dollar today. The assumption implicit in this common-sense choice is that having the use of money for a period of time, like having the use of an apartment or a car, has value. The earlier receipt of a dollar is more valuable than a later receipt, and the difference in value between the two is called the time value of money . This positive time value of money makes the choice among various intertemporal economic plans dependent not only on the magnitudes of receipts and expenditures associated with each of the plans but also upon the timing of these inflows and outflows. Virtually every area in Finance involves the solution of such intertemporal choice problems, and hence a fundamental understanding of the time value of money is an essential prerequisite to the study of Finance. It is, therefore, natural to begin with those basic definitions and analytical tools required to develop this fundamental understanding. The formal analysis, sometimes called the arithmetic of compound interest, is not difficult, and indeed many of the formulas to be derived may be quite familiar. However, the assumptions upon which the formulas are based may not be so familiar. Because these formulas are so fundamental and because their valid application depends upon the underlying assumptions being satisfied, it is appropriate to derive them in a careful and axiomatic fashion. Then, armed with these analytical tools, we can proceed in subsequent sections with the systematic development of finance theory. Although the emphasis of this section is on developing the formulas, many of the specific problems used to illustrate their application are of independent substantive importance. A positive time value of money implies that rents are paid for the use of money. For goods and services, the most common form of quoting rents is to give a money rental rate which is the dollar rent per unit time per unit item rented. A typical example would be the rental rate on an apartment which might be quoted as "$200 per month (per apartment)." However, a rental rate can be denominated in terms of any commodity or service. For example, the wheat rental rate
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Finance Theory 9 would have the form of so many bushels of wheat rent per unit item rented. So the wheat rental rate on an apartment might be quoted as "125 bushels of wheat per month (per apartment)." In the special case when the unit of payment is the same as the item rented, the rental rate is called the own rental rate , and is quoted as a pure percentage per unit time. So, for example, if the wheat rental rate on wheat were ".01 bushels of wheat per month per bushel of wheat rented," then the rental rate would simply be stated as "1 percent per month." In general, the own rental
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This note was uploaded on 06/16/2008 for the course ECON 131 taught by Professor Fasd during the Spring '08 term at Boston Conservatory.

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Merton-Chpt2 - II. ON THE ARITHMETIC OF COMPOUND INTEREST:...

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