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# EYK17_1 - E x t e n d Yo u r K n o w l e d g e 1 7 1...

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E x t e n d Y o u r K n o w l e d g e 1 7 - 1 : P r e s e n t V a l u e s The concepts of present value are described and applied in Chapter 17. This supplement provides added explanations, illustrations, calculations, present value tables, and additional assignments. P r e s e n t V a l u e C o n c e p t s There’s an old saying, time is money . This saying reflects the notion that as time passes, the assets and liabilities we hold are changing, due to interest. Interest is the payment to the owner of an asset for its use by a borrower. The most common example of this type of asset is a savings account. As we keep a balance of cash in our account, it earns interest that is paid to us by the financial institution. An example of a liability is a car loan. As we carry the balance of the loan, we accu- mulate interest costs on this debt. We must ultimately repay this loan with interest. Present value computations are a means for us to estimate the interest com- ponent of holding assets or liabilities over time. The present value of an amount applies when we either lend or borrow an asset that must be repaid in full at some future date, and we want to know its worth today. The first section focuses on the present value of a single amount. The next section will focus on the present value of a series of amounts (or annuity). LO 1 Describe the earning of interest and the concept of present value. Learning Objectives LO 1 Describe the earning of interest and the concept of present value. LO 2 Apply present value concepts to a single amount by using interest tables. LO 3 Apply present value concepts to an annuity by using interest tables.

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P r e s e n t V a l u e o f a S i n g l e A m o u n t We graphically express the present value ( p ) of a single future amount ( f ) received or paid at a future date in Exhibit PV17.1. The formula to calculate the present value of this single amount is shown in Exhibit PV17.2 where: p present value; ƒ future value; i rate of interest per period; and n number of periods. To illustrate the application of this formula, let’s assume we need \$220 one period from today. We want to know how much must be invested now, for one period, at an interest rate of 10% to provide for this \$220. 1 For this illustration the p , or present value, is the unknown amount. In particular, the present and future values, along with the interest rate, are shown graphically as: Conceptually, we know p must be less than \$220. This is obvious from the answer to the question: Would we rather have \$220 today or \$220 at some future date? If we had \$220 today, we could invest it and see it grow to something more than \$220 in the future. Therefore, if we were promised \$220 in the future, we would take less than \$220 today. But how much less? To answer that question, we can calculate an estimate of the present value of the \$220 to be received one period from now using the formula in Exhibit PV17.2 as: This means we are indifferent between \$200 today or \$220 at the end of one period.
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