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Unformatted text preview: The Time Value The Time Value of Money of Money Chapter Chapter F8 F8 8  2 1. Define future and present value. 2. Determine the future value of a single amount invested at the present time. 3. Determine the future value of an annuity. 4. Determine the present value of a single amount to be received in the future. 5. Determine the present value of an annuity. 6. Determine investment values and interest expense or revenue for various periods. Objectives Objectives 8  3 Future Value Future Value The future value of an amount is how much it will grow to at a particular time in the future. Obj  1 8  4 Present Value Present Value The present value of a future amount is the value of that amount at a particular date prior to the time the amount is paid or received. Obj  1 8  5 Future Value Future Value Future Value = Present Value (1 + R) Future Value = $1,000 (1.05) Future Value = $1,050 If $1,000 is invested on January 1, 2007, at 5% interest, what will be the future value (the amount that will accumulate) by December 31, 2007? Obj  1 8  6 Compound Interest Compound Interest If the accumulated amount ($1,050) is left in the savings account for a second year, until December 31, 2008, how much would the investment be worth at that time? $1,050(1.05) = $1,102.50 Obj  2 8  7 Compound Interest Compound Interest Interest earned in one period on interest earned in an earlier period is known as compound interest . Obj  2 8  8 Compound Interest Compound Interest Assume you invest $500 for three years at 8% interest. How much would your investment be worth at the end of three years? FV = PV(1 + R) t FV = $500(1.08)³ FV = $629.86 Obj  2 8  9 Compound Interest Compound Interest 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 Period 1.010 1.020 1.030 1.040 1.050 1.060 1.070 1.080 1.090 1.020 1.040 1.061 1.082 1.103 1.224 1.145 1.164 1.188 1.030 1.061 1.093 1.125 1.158 1.191 1.225 1.260 1.295 1 2 3 0.08 Interest Rate Interest Rate 1.260 1.260 FV = $500 x 1.260 = $630 (rounded) To calculate a future value, a future value of a single amount table, such as the one below, can be used . Obj  2 8  10 A B C D A B C D Value at Value at Interest Earned Interest Earned FV at End FV at End Year Year Beginning of Year Beginning of Year (B x Interest Paid) (B x Interest Paid) (B + C) (B + C) Interest Table for an Investment of $500 for Three Years at 8% 1 500.00 40.00 540.00 2 540.00 43.20 583.20 3 583.20 46.66 629.86 Total Total 129.86 129.86 Exhibit 1 Exhibit 1 Obj  2 8  11 An annuity is a series of equal amounts received or paid over a specified number of equal time periods. Future Value of an Annuity Future Value of an Annuity Obj  3 8  12 If $500 is invested at the end of each year for three years, how much would the investment be worth at the end of three years if the interest earned is 8% per year?...
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 Spring '07
 Verduzco
 Time Value Of Money

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