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# CH04 - Chapter 4 Time Value of Money 4-1 Example of a Time...

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4-1 Chapter 4 Time Value of Money

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4-2 Example of a Time Line Points in time Time 3 2 1 0 1 2 3 Periods
4-3 Time Line 1 + R 1 0 1 1 1.10 Flat Term Structure—One Period

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4-4 Time Line 1 + R 2 0 1 1 (1 + R)(1 + R) Flat Term Structure—Two Periods
4-5 . 21 . 1 01 . 0 20 . 0 1 ) 10 . 0 ( ) 10 . 0 ( 2 1 ) 10 . 1 ( R R 2 1 ) R 1 ( 2 time at value Future 2 2 2 2 = + + = + + = + + = + =

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4-6 Future Value of One Dollar Received at Time 0 N = Number of periods I/YR = Interest rate PMT = 0 FV = ? PV = -1
4-7 Time Line 3 2 1 0 PV 1 = 3 ) R 1 ( 1 + 2 ) R 1 ( 1 + 1 ) R 1 ( 1 + PV 2 = PV 3 = Present Value

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4-8 Present Value of One Dollar N = Number of periods I/YR = Interest rate PMT = 0 FV = 1 PV = -Price
4-9 Present Value of \$1 1 0.9901 0.9804 0.9709 0.9615 0.9524 0.9434 0.9346 0.9259 0.9174 0.9091 2 0.9803 0.9612 0.9426 0.9246 0.9070 0.8900 0.8734 0.8573 0.8417 0.8264 3 0.9706 0.9423 0.9151 0.8890 0.8638 0.8396 0.8163 0.7938 0.7722 0.7513 4 0.9610 0.9238 0.8885 0.8548 0.8227 0.7921 0.7629 0.7350 0.7084 0.6830 5 0.9515 0.9057 0.8626 0.8219 0.7835 0.7473 0.7130 0.6806 0.6499 0.6209 6 0.9420 0.8880 0.8375 0.7903 0.7462 0.7050 0.6663 0.6302 0.5963 0.5645 7 0.9327 0.8706 0.8131 0.7599 0.7107 0.6651 0.6227 0.5835 0.5470 0.5132 8 0.9235 0.8535 0.7894 0.7307 0.6768 0.6274 0.5820 0.5403 0.5019 0.4665 9 0.9143 0.8368 0.7664 0.7026 0.6446 0.5919 0.5439 0.5002 0.4604 0.4241 10 0.9053 0.8203 0.7441 0.6756 0.6139 0.5584 0.5083 0.4632 0.4224 0.3855 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

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4-10 Annuities Suppose that there is an annuity of 1 dollar at each future point in time. 3 2 1 0 \$1 Time . . . n . . . \$1 \$1 \$1
4-11 In the case of an annuity for 2 periods, the present value is . 74 . 1 \$ ) 10 . 1 ( 1 10 . 1 1 ) R 1 ( 1 R 1 1 lue Present Va 2 2 = + = + + + =

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4-12 n 2 ) R 1 ( 1 ) R 1 ( 1 R 1 1 PVA annuity of value Present + + + + + + = = . n time at \$1 PV 2 time at \$1 PV 1 time at \$1 PV + + + = . ) R 1 ( 1 1 R 1 PVA n + - =
4-13 Present Value of a 1 Dollar Annuity N = Number of periods I/YR = Interest rate PMT = 1 FV = 0 PV = ?

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4-14 Present Value of an Annuity of \$1 1 0.9901 0.9804 0.9709 0.9615 0.9524 0.9434 0.9346 0.9259 0.9174 0.9091 2 1.9704 1.9416 1.9135 1.8861 1.8594 1.8334 1.8080 1.7833 1.7591 1.7355 3 2.9410 2.8839 2.8286 2.7751 2.7232 2.6730 2.6243 2.5771 2.5313 2.4869 4 3.9020 3.8077 3.7171 3.6299 3.5460 3.4651 3.3872 3.3121 3.2397 3.1688 5 4.8534 4.7135 4.5797 4.4518 4.3295 4.2124 4.1002 3.9927 3.8897 3.7908 6 5.7955 5.6014 5.4172 5.2421 5.0757 4.9173 4.7665 4.6229 4.4859 4.3553 7 6.7282 6.4720 6.2303 6.0021 5.7864 5.5824 5.3893 5.2064 5.0330 4.8684 8 7.6517 7.3255 7.0197 6.7327 6.4632 6.2098 5.9713 5.7466 5.5648 5.3349 9 8.5660 8.1622 7.7861 7.4353 7.1078 6.8017 6.5152 6.2469 5.9952 5.7590 10 9.4713 8.9826 8.5302 8.1109 7.7217 7.3601 7.0236 6.7101 6.4177 6.1446 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%
4-15 Future Value of a 1 Dollar Annuity N = Number of periods I/YR = Interest rate PMT = 1 FVA = ?

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