Time Value of Money Concept
Time Value of Money Concept The following situations involve the application of the time value of money concept. Use the full factor when calculating your results. Use the appropriate present or future value table: FV of $1, PV of $1, FV of Annuity of $1 and PV of Annuity of $1 1. Janelle Carter deposited $9,890 in the bank on January 1, 2000, at an interest rate of 10% compounded annually. How much has accumulated in the account by January 1, 2017? Round to the nearest whole dollar. $ 2. Mike Smith deposited $24,130 in the bank on January 1, 2007. On January 2, 2017, this deposit has accumulated to $52,095. Interest is compounded annually on the account. What rate of interest did Mike earn on the deposit? Round to the nearest whole percent. X % 3. Lee Spony made a deposit in the bank on January 1, 2010. The bank pays Interest at the rate of 12% compounded annually. On January 1, 2017, the deposit has accumulated to $12,380. How much money did Lee originally deposit on January1, 2010? Round to the nearest whole dollar. $ 4. Nancy Holmes deposited $5,170 in the bank on January 1 a few years ago. The bank pays an interest rate of 10% compounded annually, and the deposit is now worth $11,082. How many years has the deposit been invested? Round to the nearest whole year. X years TABLE 9-1 Future Value of $1 (N) Periods 2% 3% 4% 5% 6% 7% 8% 10% 12% 15% 1 1.06000 1.03000 1.06090 2 1.12360 1.02000 1.04040 1.06121 1.08243 1.07000 1.14490 1.22504 1.31080 1.04000 1.08160 1.12486 1.16986 1.21665 1.10000 1.21000 1.33100 1.46410 3 1.09273 1.19102 1.26248 4 5 1.12551 1.15927 1.12000 1.25440 1.40493 1.57352 1.76234 1.97382 2.21068 2.47596 1.33823 1.40255 6 1.19405 1.26532 1.50073 7 1.22987 1.31593 1.60578 1.61051 1.77156 1.94872 2.14359 2.35795 2.59374 1.08000 1.16640 1.25971 1.36049 1.46933 1.58687 1.71382 1.85093 1.99900 2.15892 2.33164 2.51817 2.71962 2.93719 8 9 10 1.26677 1.30477 1.34392 1.38423 1.42576 1.71819 1.83846 1.96715 2.10485 2.25219 2.77308 3.10585 3.47855 3.89598 11 12 1.41852 1.50363 1.59385 1.68948 1.79085 1.89830 2.01220 2.13293 2.26090 2.39656 2.54035 2.69277 2.85434 1.05000 1.10250 1.15763 1.21551 1.27628 1.34010 1.40710 1.47746 1.55133 1.62889 1.71034 1.79586 1.88565 1.97993 2.07893 2.18287 2.29202 2.40662 2.52695 2.65330 2.92526 3.22510 3.55567 3.92013 1.10408 1.12616 1.14869 1.17166 1.19509 1.21899 1.24337 1.26824 1.29361 1.31948 1.34587 1.37279 1.40024 1.42825 1.45681 1.48595 1.54598 1.60844 1.36857 1.42331 1.48024 1.53945 1.60103 1.66507 1.73168 1.80094 1.87298 1.94790 13 4.36349 14 15 1.15000 1.32250 1.52088 1.74901 2.01 136 2.31306 2.66002 3.05902 3.51788 4.04556 4.65239 5.35025 6.15279 7.07571 8.13706 9.35762 10.76126 12.37545 14.23177 16.36654 21.64475 28.62518 37.85680 50.06561 66.21177 2.40985 2.57853 2.75903 2.95216 3.15882 1.46853 1.51259 1.55797 1.60471 1.65285 1.70243 1.75351 1.80611 1.91610 16 2.85312 3.13843 3.45227 3.79750 4.17725 4.59497 5.05447 5.55992 6.11591 6.72750 8.14027 3.17217 3.42594 3.70002 4.88711 5.47357 6.13039 6.86604 7.68997 8.61276 17 18 2.02582 2.10685 19 3.02560 3.37993 3.61653 3.86968 20 2.19112 3.20714 9.64629 22 2.36992 3.60354 4.04893 4.43040 5.07237 3.99602 4.31570 4.66096 5.43654 6.34118 7.39635 8.62711 10.06266 24 2.03279 2.56330 9.84973 26 2.77247 1.67342 1.74102 2.15659 2.28793 2.42726 28 4.54938 5.11169 5.74349 2.99870 3.24340 12.10031 15.17863 19.04007 23.88387 29.95992 5.80735 6.64884 7.61226 11.91818 14.42099 17.44940 30 1.81136 4.32194 TABLE 9-2 Present Value of $1 (N) Periods 2% 3% 4% 5% 6% 7% 8% 10% 12% 15% 1 .96154 .93458 92593 .89286 .86957 2 .95238 .90703 .86384 .92456 .88900 .79719 .87344 .81630 3 .71 178 4 .85480 .76290 .63552 97087 94260 91514 .88849 .86261 .83748 .81309 .78941 5 .82193 .71299 98039 .96117 94232 .92385 .90573 .88797 .87056 .85349 .83676 .82035 56743 .94340 .89000 .83962 .79209 .74726 .70496 .66506 .62741 .59190 .55839 .85734 .79383 .73503 68058 .63017 .58349 .54027 6 .66634 50663 .82270 .78353 .74622 .71068 .67684 .64461 .61391 .79031 .75992 .73069 7 .75614 .65752 .57175 49718 43233 37594 32690 28426 24718 45235 8 40388 9 .76642 .70259 .36061 50025 46319 10 .74409 11 .80426 .67556 .64958 .62480 .58468 42888 on 2 3 .62275 .58201 .54393 .50835 .47509 44401 .41496 .38782 .36245 21494 .90909 .82645 .75131 .68301 .62092 56447 -51316 .46651 42410 .38554 .35049 .31863 28966 26333 .23939 .21763 .19784 .17986 .16351 . 14864 .12285 .32197 .28748 .25668 22917 12 .52679 49697 46884 44230 .78849 .55684 .18691 13 .77303 .60057 .16253 14 .14133 .75788 .74301 .57748 .55526 .39711 .36770 34046 31524 29189 .27027 15 41727 .12289 .53032 .50507 48102 45811 43630 41552 20462 18270 .16312 .14564 .53391 .39365 .33873 .10686 16 17 .72845 .71416 .72242 .70138 .68095 .66112 .64186 .62317 .60502 .58739 .57029 .55368 52189 49193 46369 43708 37136 .31657 18 .29586 .13004 .51337 49363 47464 45639 35034 33051 .25025 .23171 19 .27651 20 39573 37689 34185 .09293 .08081 .07027 .06110 .04620 .03493 .70016 .68643 .67297 .64684 .62172 .59758 .57437 31180 25842 .22571 22 24 26 27751 .11611 .10367 .08264 .06588 .05252 .42196 39012 36069 33348 30832 31007 21455 .18394 . 15770 .13520 .11591 09938 24698 21981 .19583 .19715 . 17220 .15040 .13137 28124 25509 23138 .10153 .08391 .06934 28 .04187 .03338 .02642 .01997 .01510 30 .55207 41199 .17411 .05731 TABLE 9-3 Future Value of Annuity of $1 (N) Periods 2% 3% 4% 5% 6% 7% 8% 10% 12% 15% 1.00000 1.00000 1.00000 1 2 2.04000 2.07000 2.08000 1.00000 2.02000 3.06040 4.12161 1.00000 2.03000 3.09090 4.18363 1.00000 2.06000 3.18360 4.37462 3 1.00000 2.05000 3.15250 4.31013 5.52563 3.21490 3.24640 1.00000 2.12000 3.37440 4.77933 6.35285 3.12160 4.24646 5.41632 6.63298 4 4.50611 5 5.20404 5.30914 5.63709 5.86660 4.43994 5.75074 7.15329 8.65402 6 6.46841 6.80191 8.11519 7 6.30812 7.43428 8.58297 7.66246 6.97532 8.39384 9.89747 8 9 7.89829 9.21423 10.58280 12.00611 13.48635 15.02581 8.89234 10.15911 11.46388 12.80780 9.75463 1.00000 2.15000 3.47250 4.99338 6.74238 8.75374 11.06680 13.72682 16.78584 20.30372 24.34928 29.00167 34.35192 7.33593 8.92280 10.63663 12.48756 14.48656 8.14201 9.54911 11.02656 12.57789 14.20679 15.91713 17.71298 10.25980 11.97799 13.81645 15.78360 11.49132 13.18079 10.08901 12.29969 14.77566 17.54874 20.65458 10 10.94972 12.16872 13.41209 11 14.97164 16.64549 12 18.97713 14.19203 15.61779 16.86994 18.88214 13 14.68033 16.62684 21.49530 1.00000 2.10000 3.31000 4.64100 6.10510 7.71561 9.48717 11.43589 13.57948 15.93742 18.53117 21.38428 24.52271 27.97498 31.77248 35.94973 40.54470 45.59917 51.15909 57.27500 71.40275 88.49733 109.18177 134.20994 164.49402 17.88845 20.14064 22.55049 25.12902 24.13313 28.02911 32.39260 37.27971 14 21.01507 15.97394 17.29342 18.29191 20.02359 19.59863 21.57856 15 16 17 42.75328 18.63929 20.01207 21.82453 23.69751 24.21492 27.15211 30.32428 33.75023 37.45024 23.65749 25.84037 18 40.50471 47.58041 55.71747 65.07509 75.83636 88.21181 102.44358 21.41231 19 22.84056 17.08632 18.59891 20.15688 21.76159 23.41444 25.11687 26.87037 30.53678 34.42647 38.55304 42.93092 47.57542 41.44626 20 23.27597 25.67253 28.21288 30.90565 33.75999 36.78559 43.39229 50.81558 59.15638 68.52811 79.05819 25.64541 27.67123 29.77808 34.24797 39.08260 44.31174 49.96758 56.08494 24.29737 27.29898 30.42186 33.67091 37.05121 40.56808 22 28.13238 30.53900 33.06595 38.50521 44.50200 51.11345 58.40258 66.43885 27.88805 30.84022 33.99903 37.37896 40.99549 49.00574 58.17667 68.67647 80.69769 94.46079 24 48.88367 55.74971 63.43968 72.05244 92.50258 118.15524 150.33393 190.69889 241.33268 45.76196 55.45676 66.76476 79.95442 95.33883 113.28321 137.63164 184.16784 245.71197 327.10408 26 28 30 434.74515 6% 7% 8% 10% 12% 15% .93458 1.80802 .92593 1.78326 .90909 1.73554 2.48685 3.16987 .89286 1.69005 2.40183 .86957 1.62571 2.28323 2.85498 2.62432 2.57710 3.31213 .94340 1.83339 2.67301 3.46511 4.21236 4.91732 5.58238 6.20979 3.03735 3.60478 3.79076 3.99271 4.62288 3.35216 3.78448 4.35526 4.86842 TABLE 9-4 Present Value of Annuity of $1 (N) Periods 2% 3% 4% 5% 1 .98039 .97087 .96154 .95238 2 1.94156 1.91347 1.88609 1.85941 3 2.88388 2.82861 2.77509 2.72325 4 3.80773 3.71710 3.62990 3.54595 5 4.71346 4.57971 4.45182 4.32948 6 5.60143 5.41719 5.24214 5.07569 7 6.47199 6.23028 6.00205 5.78637 8 7.32548 7.01969 6.73274 6.46321 9 8.16224 7.78611 7.43533 7.10782 10 8.98259 8.53020 8.11090 7.72173 11 9.78685 9.25262 8.76048 8.30641 12 10.57534 9.95400 9.38507 8.86325 13 11.34837 10.63496 9.98565 9.39357 12.10625 11.29607 10.56312 9.89864 15 12.84926 11.93794 11.11839 10.37966 16 13.57771 12.56110 11.65230 10.83777 17 14.29187 13.16612 12.16567 11.27407 18 14.99203 13.75351 12.65930 11.68959 19 15.67846 14.32380 13.13394 12.08532 20 16.35143 14.87747 13.59033 12.46221 22 17.65805 15.93692 14.45112 13.16300 24 18.91393 16.93554 15.24696 13.79864 26 20.12104 17.87684 15.98277 14.37519 21.28127 18.76411 16.66306 14.89813 30 22.39646 19.60044 17.29203 15.37245 4.11141 4.56376 4.96764 5.32825 5.65022 5.20637 5.74664 6.24689 6.71008 7.13896 7.53608 6.80169 7.36009 7.88687 8.38384 7.90378 8.24424 3.38721 4.10020 4.76654 5.38929 5.97130 6.51523 7.02358 7.49867 7.94269 8.35765 8.74547 9.10791 9.44665 9.76322 10.05909 10.33560 10.59401 11.06124 11.46933 11.82578 12.13711 12.40904 4.16042 4.48732 4.77158 5.01877 5.23371 5.42062 5.58315 5.72448 5.84737 5.95423 5.33493 5.75902 6.14457 6.49506 6.81369 7.10336 7.36669 7.60608 7.82371 8.02155 8.20141 8.85268 9.29498 9.71225 10.10590 10.47726 10.82760 11.15812 11.46992 14 5.93770 6.19437 6.42355 6.62817 6.81086 6.97399 7.11963 6.04716 8.55948 8.85137 9.12164 9.37189 9.60360 9.81815 7.24967 7.36578 6.12797 6.19823 8.36492 7.46944 6.25933 10.20074 7.64465 12.04158 12.55036 13.00317 13.40616 10.52876 10.80998 11.05108 11.25778 8.51356 8.77154 8.98474 9.16095 9.30657 7.78432 7.89566 7.98442 8.05518 6.35866 6.43377 6.49056 6.53351 6.56598 28 13.76483 9.42691
