slides06 - 6. Time value of money We will review the tools...

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Unformatted text preview: 6. Time value of money We will review the tools for discounting cash flows. Simple interest With simple interest, the amount earned each period is always the same: i = rp o where i = interest earned r = interest rate (per period) p o = principal Therefore, at the end of n periods, we will have (principal plus interest) p t = p o + trp o = p o (1 + tr ) 2 Example If we invest $100 at 10% simple interest for 7 years, how much will we have? Solution: 100 1 . 7 = 170 3 Compound interest With compound interest, we earn interest not only on the principal but also on the interest earned in previous periods: p 1 = p o + rp o = p o (1 + r ) p 2 = p 1 (1 + r ) = p o (1 + r ) 2 p 3 = p 2 (1 + r ) = p o (1 + r ) 3 . . . p t = p t- 1 (1 + r ) = p o (1 + r ) t 4 Example If we invest $100 at 10% compound interest for 7 years, how much will we have? How much of the interest earned in the previous example was from the principal, and how much was earned on previous periods in- terest? Solution: The total will be 100 1 . 1 7 = 194 . 87 , of which 194 . 87- 170 = 24 . 87 is interest on interest. 5 Simple vs compound interest 6 Compounding over many periods Because of compounding, small differences in interest rate can make a large difference after many periods. 7 Present value and future value The value of an investment at present is often referred to as the present value (PV) . Its value in the future is often referred to as its future value (FV) . Thus, one might also write the formula for compound interest as FV t = PV (1 + r ) t 8 Discounting Computing the present value of a future cash flow is often referred to as discounting the cash flow. By rearranging the previous formula, we get PV = FV t (1 + r ) t 9 Four variables There are four variables in the equation FV t = PV (1 + r ) t . Given values for any three, we can solve for the fourth. It is not hard to do this algebraically. But, it is easier to use our financial calculators. 10 Calculators There are a couple of things to be careful about when using your calculators: Be sure that you are in end mode rather than begin mode. This means that payments are at the end rather than the beginning of each period. This is the standard convention unless noted otherwise. Be sure that the number of payments per period is set to 1. 11 Example Suppose I invest $100 initially. After 8 years, the investment is worth $190. What interest rate did I earn (assume annual com- pounding)?...
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This note was uploaded on 03/31/2008 for the course FNCE 3010 taught by Professor Donchez,ro during the Fall '07 term at Colorado.

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slides06 - 6. Time value of money We will review the tools...

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