Steffi Derr expects to invest $16,000 annually that will earn 10%. How many annual investments must Derr make to accumulate $729,587 on the date of the last investment? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided. Round "Table Factor" to 4 decimal places.) Future Value Annuity Payment Table Factor Annual Investments investments Exercise B-18 Practical applications of the time value of money LO P1, P2, P3, P4 Provided are links to the present and future value tables: (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided. Round your answer to the nearest whole dollar.) a. How much would you have to deposit today if you wanted to have $42,000 in three years? Annual interest rate is 10%. b. Assume that you are saving up for a trip around the world when you graduate in two years. If you can earn 6% on your investments, how much would you have to deposit today to have $10,500 when you graduate? (Round your answer to 2 decimal places.) c-1. Calculate the future value of an investment of $499 for ten years earning an interest of 9%. (Round your answer to 2 decimal places.) c-2. Would you rather have $499 now or $1,000 ten years from now? d. Assume that a college parking sticker today costs $62. If the cost of parking is increasing at the rate of 6% per year, how much will the college parking sticker cost in seven years? (Round your answer to 2 decimal places.) e. Assume that the average price of a new home is $110,000. If the cost of a new home is increasing at a rate of 7% per year, how much will a new home cost in eight years? (Round your answer to 2 decimal places.) f. An investment will pay you $5,500 in 10 years, and it will also pay you $210 at the end of each of the next 10 years (years 1 thru 10). If the annual interest rate is 6%, how much would you be willing to pay today for this type of investment? (Round your intermediate calculations and final answer to the nearest whole dollar.) g. A college student is reported in the newspaper as having won $6,000,000 in the Kansas State Lottery. However, as is often the custom with lotteries, she does not actually receive the entire $6 million now. Instead she will receive $300,000 at the end of the year for each of the next 20 years. If the annual interest rate is 7%, what is the present value (today's amount') that she won? (ignore taxes). (Round your answer to nearest whole dollar.) X Answer is not complete. a $ Present value Present value 31,555 9,345.00 b $ C Future value $ 1,181.33 Now 2 d. $ Would you rather have $499 now or $1,000 ten years from now? Future value Future value Present value 93.22 e f. g. Present value TABLE B.1 Present Value of 1 p=1/(1 + i)" Rate Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 15% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 0.9901 0.9803 0.9706 0.9610 0.9515 0.9420 0.9327 0.9235 0.9143 0.9053 0.8963 0.8874 0.8787 0.8700 0.8613 0.8528 0.8444 0.8360 0.8277 0.8195 0.7798 0.7419 0.7059 0.6717 0.9804 0.9612 0.9423 0.9238 0.9057 0.8880 0.8706 0.8535 0.8368 0.8203 0.8043 0.7885 0.7730 0.7579 0.7430 0.7284 0.7142 0.7002 0.6864 0.6730 0.6095 0.5521 0.5000 0.4529 0.9709 0.9426 0.9151 0.8885 0.8626 0.8375 0.8131 0.7894 0.7664 0.7441 0.7224 0.7014 0.6810 0.6611 0.6419 0.6232 0.6050 0.5874 0.5703 0.5537 0.4776 0.4120 0.3554 0.3066 0.9615 0.9246 0.8890 0.8548 0.8219 0.7903 0.7599 0.7307 0.7026 0.6756 0.6496 0.6246 0.6006 0.5775 0.5553 0.5339 0.5134 0.4936 0.4746 0.4564 0.3751 0.3083 0.2534 0.2083 0.9524 0.9070 0.8638 0.8227 0.7835 0.7462 0.7107 0.6768 0.6446 0.6139 0.5847 0.5568 0.5303 0.5051 0.4810 0.4581 0.4363 0.4155 0.3957 0.3769 0.2953 0.2314 0.1813 0.1420 0.9434 0.8900 0.8396 0.7921 0.7473 0.7050 0.6651 0.6274 0.5919 0.5584 0.5268 0.4970 0.4688 0.4423 0.4173 0.3936 0.3714 0.3503 0.3305 0.3118 0.2330 0.1741 0.1301 0.0972 0.9346 0.8734 0.8163 0.7629 0.7130 0.6663 0.6227 0.5820 0.5439 0.5083 0.4751 0.4440 0.4150 0.3878 0.3624 0.3387 0.3166 0.2959 0.2765 0.2584 0.1842 0.1314 0.0937 0.0668 0.9259 0.8573 0.7938 0.7350 0.6806 0.6302 0.5835 0.5403 0.5002 0.4632 0.4289 0.3971 0.3677 0.3405 0.3152 0.2919 0.2703 0.2502 0.2317 0.2145 0.1460 0.0994 0.0676 0.0460 0.9174 0.8417 0.7722 0.7084 0.6499 0.5963 0.5470 0.5019 0.4604 0.4224 0.3875 0.3555 0.3262 0.2992 0.2745 0.2519 0.2311 0.2120 0.1945 0.1784 0.1160 0.0754 0.0490 0.0318 0.9091 0.8264 0.7513 0.6830 0.6209 0.5645 0.5132 0.4665 0.4241 0.3855 0.3505 0.3186 0.2897 0.2633 0.2394 0.2176 0.1978 0.1799 0.1635 0.1486 0.0923 0.0573 0.0356 0.0221 0.8929 0.7972 0.7118 0.6355 0.5674 0.5066 0.4523 0.4039 0.3606 0.3220 0.2875 0.2567 0.2292 0.2046 0.1827 0.1631 0.1456 0.1300 0.1161 0.1037 0.0588 0.0334 0.0189 0.0107 0.8696 0.7561 0.6575 0.5718 0.4972 0.4323 0.3759 0.3269 0.2843 0.2472 0.2149 0.1869 0.1625 0.1413 0.1229 0.1069 0.0929 0.0808 0.0703 0.0611 0.0304 0.0151 0.0075 0.0037 *Used to compute the present value of a known future amount. For example: How much would you need to invest today at 10% compounded semiannually to accumulate $5.000 in 6 years from today? Using the factors of n= 12 and i = 5% (12 semiannual periods and a semiannual rate of 5), the factor is 0.5568. You would need to invest $2,784 today ($5,000x0.5568). TABLE B.2 Future Value of 1 f=(1 + i)" Rate Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 15% 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 1.0000 1.0100 1.0201 1.0303 1.0406 1.0510 1.0615 1.0721 1.0829 1.0937 1.1046 1.1157 1.1268 1.1381 1.1495 1.1610 1.1726 1.1843 1.1961 1.2081 1.2202 1.2824 1.3478 1.4166 1.4889 1.0000 1.0200 1.0404 1.0612 1.0824 1.1041 1.1262 1.1487 1.1717 1.1951 1.2190 1.2434 1.2682 1.2936 1.3195 1.3459 1.3728 1.4002 1.4282 1.4568 1.4859 1.6406 1.8114 1.9999 2.2080 1.0000 1.0300 1.0609 1.0927 1.1255 1.1593 1.1941 1.2299 1.2668 1.3048 1.3439 1.3842 1.4258 1.4685 1.5126 1.5580 1.6047 1.6528 1.7024 1.7535 1.8061 2.0938 2.4273 2.8139 3.2620 1.0000 1.0400 1.0816 1.1249 1.1699 1.2167 1.2653 1.3159 1.3686 1.4233 1.4802 1.5395 1.6010 1.6651 1.7317 1.8009 1.8730 1.9479 2.0258 2.1068 2.1911 2.6658 3.2434 3.9461 4.8010 1.0000 1.0500 1.1025 1.1576 1.2155 1.2763 1.3401 1.4071 1.4775 1.5513 1.6289 1.7103 1.7959 1.8856 1.9799 2.0789 2.1829 2.2920 2.4066 2.5270 2.6533 3.3864 4.3219 5.5160 7.0400 1.0000 1.0600 1.1236 1.1910 1.2625 1.3382 1.4185 1.5036 1.5938 1.6895 1.7908 1.8983 2.0122 2.1329 2.2609 2.3966 2.5404 2.6928 2.8543 3.0256 3.2071 4.2919 5.7435 7.6861 10.2857 1.0000 1.0700 1.1449 1.2250 1.3108 1.4026 1.5007 1.6058 1.7182 1.8385 1.9672 2.1049 2.2522 2.4098 2.5785 2.7590 2.9522 3.1588 3.3799 3.6165 3.8697 5.4274 7.6123 10.6766 14.9745 1.0000 1.0800 1.1664 1.2597 1.3605 1.4693 1.5869 1.7138 1.8509 1.9990 2.1589 2.3316 2.5182 2.7196 2.9372 3.1722 3.4259 3.7000 3.9960 4.3157 4.6610 6.8485 10.0627 14.7853 21.7245 1.0000 1.0900 1.1881 1.2950 1.4116 1.5386 1.6771 1.8280 1.9926 2.1719 2.3674 2.5804 2.8127 3.0658 3.3417 3.6425 3.9703 4.3276 4.7171 5.1417 5.6044 8.6231 13.2677 20.4140 31.4094 1.0000 1.1000 1.2100 1.3310 1.4641 1.6105 1.7716 1.9487 2.1436 2.3579 2.5937 2.8531 3.1384 3.4523 3.7975 4.1772 4.5950 5.0545 5.5599 6.1159 6.7275 10.8347 17.4494 28.1024 45.2593 1.0000 1.1200 1.2544 1.4049 1.5735 1.7623 1.9738 2.2107 2.4760 2.7731 3.1058 3.4785 3.8960 4.3635 4.8871 5.4736 6.1304 6.8660 7.6900 8.6128 9.6463 17.0001 29.9599 52.7996 93.0510 1.0000 1.1500 1.3225 1.5209 1.7490 2.0114 2.3131 2.6600 3.0590 3.5179 4.0456 4.6524 5.3503 6.1528 7.0757 8.1371 9.3576 10.7613 12.3755 14.2318 16.3665 32.9190 66.2118 133.1755 267.8635 Used to compute the future value of a known present amount. For example: What is the accumulated value of $3,000 invested today at 8. compounded quarterly for 5 years? Using the factors of n=20 and i= 2% (20 quarterly periods and a quarterly interest rate of 2), the factor is 1.4859. The accumulated value is $4,457.70 ($3.000 x 1.4859). -=[1-a + li (1 + i)" TABLE B.3: Present Value of an Annuity of 1 Rate Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 15% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 0.9901 1.9704 2.9410 3.9020 4.8534 5.7955 6.7282 7.6517 8.5660 9.4713 10.3676 11.2551 12.1337 13.0037 13.8651 14.7179 15.5623 16.3983 17.2260 18.0456 22.0232 25.8077 29.4086 32.8347 0.9804 1.9416 2.8839 3.8077 4.7135 5.6014 6.4720 7.3255 8.1622 8.9826 9.7868 10.5753 11.3484 12.1062 12.8493 13.5777 14.2919 14.9920 15.6785 16.3514 19.5235 22.3965 24.9986 27.3555 0.9709 1.9135 2.8286 3.7171 4.5797 5.4172 6.2303 7.0197 7.7861 8.5302 9.2526 9.9540 10.6350 11.2961 11.9379 12.5611 13.1661 13.7535 14.3238 14.8775 17.4131 19.6004 21.4872 23.1148 0.9615 1.8861 2.7751 3.6299 4.4518 5.2421 6.0021 6.7327 7.4353 8.1109 8.7605 9.3851 9.9856 10.5631 11.1184 11.6523 12.1657 12.6593 13.1339 13.5903 15.6221 17.2920 18.6646 19.7928 0.9524 1.8594 2.7232 3.5460 4.3295 5.0757 5.7864 6.4632 7.1078 7.7217 8.3064 8.8633 9.3936 9.8986 10.3797 10.8378 11.2741 11.6896 12.0853 12.4622 14.0939 15.3725 16.3742 17.1591 0.9434 1.8334 2.6730 3.4651 4.2124 4.9173 5.5824 6.2098 6.8017 7.3601 7.8869 8.3838 8.8527 9.2950 9.7122 10.1059 10.4773 10.8276 11.1581 11.4699 12.7834 13.7648 14.4982 15.0463 0.9346 1.8080 2.6243 3.3872 4.1002 4.7665 5.3893 5.9713 6.5152 7.0236 7.4987 7.9427 8.3577 8.7455 9.1079 9.4466 9.7632 10.0591 10.3356 10.5940 11.6536 12.4090 12.9477 13.3317 0.9259 0.9174 1.7833 1.7591 2.5771 2.5313 3.3121 3.2397 3.9927 3.8897 4.6229 4.4859 5.2064 5.0330 5.7466 5.5348 6.2469 5.9952 6.7101 6.4177 7.1390 6.8052 7.5361 7.1607 7.9038 7.4869 8.2442 7.7862 8.5595 8.0607 8.8514 8.3126 9.1216 8.5436 9.3719 8.7556 9.6036 8.9501 9.8181 9.1285 10.6748 9.8226 11.2578 10.2737 11.6546 10.5668 11.9246 10.7574 0.9091 1.7355 2.4869 3.1699 3.7908 4.3553 4.8684 5.3349 5.7590 6.1446 6.4951 6.8137 7.1034 7.3667 7.6061 7.8237 8.0216 8.2014 8.3649 8.5136 9.0770 9.4269 9.6442 9.7791 0.8929 1.6901 2.4018 3.0373 3.6048 4.1114 4.5638 4.9676 5.3282 5.6502 5.9377 6.1944 6.4235 6.6282 6.8109 6.9740 7.1196 7.2497 7.3658 7.4694 7.8431 8.0552 8.1755 8.2438 0.8696 1.6257 2.2832 2.8550 3.3522 3.7845 4.1604 4.4873 4.7716 5.0188 5.2337 5.4206 5.5831 5.7245 5.8474 5.9542 6.0472 6.1280 6.1982 6.2593 6.4641 6.5660 6.6166 6.6418 Used to calculate the present value of a series of equal payments made at the end of each period. For example: What is the present value of $2,000 per year for 10 years assuming an annual interest rate of 98 ? For (n = 10, i = 9%), the PV factor is 6.4177. $2,000 per year for 10 years is the equivalent of $12,835 today ($2,000 X 6.4177). f=[(1 + i)" - 1]/i TABLE B.45 Future Value of an Annuity of 1 Rate Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 15% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 1.0000 2.0100 3.0301 4.0604 5.1010 6.1520 7.2135 8.2857 9.3685 10.4622 11.5668 12.6825 13.8093 14.9474 16.0969 17.2579 18.4304 19.6147 20.8109 22.0190 28.2432 34.7849 41.6603 48.8864 1.0000 2.0200 3.0604 4.1216 5.2040 6.3081 7.4343 8.5830 9.7546 10.9497 12.1687 13.4121 14.6803 15.9739 17.2934 18.6393 20.0121 21.4123 22.8406 24.2974 32.0303 40.5681 49.9945 60.4020 1.0000 2.0300 3.0909 4.1836 5.3091 6.4684 7.6625 8.8923 10.1591 11.4639 12.8078 14.1920 15.6178 17.0863 18.5989 20.1569 21.7616 23.4144 25.1169 26.8704 36.4593 47.5754 60.4621 75.4013 1.0000 1.0000 2.0400 2.0500 3.1216 3.1525 4.2465 4.3101 5.4163 5.5256 6.6330 6.8019 7.8983 8.1420 9.2142 9.5491 10.5828 11.0266 12.0061 12.5779 13.4864 14.2068 15.0258 15.9171 16.6268 17.7130 18.2919 19.5986 20.0236 21.5786 21.8245 23.6575 23.6975 25.8404 25.6454 28.1324 27.6712 30.5390 29.7781 33.0660 41.6459 47.7271 56.0849 66.4388 73.6522 90.3203 95.0255 120.7998 1.0000 2.0600 3.1836 4.3746 5.6371 6.9753 8.3938 9.8975 11.4913 13.1808 14.9716 16.8699 18.8821 21.0151 23.2760 25.6725 28.2129 30.9057 33.7600 36.7856 54.8645 79.0582 111.4348 154.7620 1.0000 2.0700 3.2149 4.4399 5.7507 7.1533 8.6540 10.2598 11.9780 13.8164 15.7836 17.8885 20.1406 22.5505 25.1290 27.8881 30.8402 33.9990 37.3790 40.9955 63.2490 94.4608 138.2369 199.6351 1.0000 1.0000 1.0000 2.0800 2.0900 2.1000 3.2464 3.2781 3.3100 4.5061 4.5731 4.6410 5.8666 5.9847 6.1051 7.3359 7.5233 7.7156 8.9228 9.2004 9.4872 10.6366 11.0285 11.4359 12.4876 13.0210 13.5795 14.4866 15.1929 15.9374 16.6455 17.5603 18.5312 18.9771 20.1407 21.3843 21.4953 22.9534 24.5227 24.2149 26.0192 27.9750 27.1521 29.3609 31.7725 30.3243 33.0034 35.9497 33.7502 36.9737 40.5447 37.4502 41.3013 45.5992 41.4463 46.0185 51.1591 45.7620 51.1601 57.2750 73.1059 84.7009 98.3471 113.2832 136.3075 164.4940 172.3168 215.7108 271.0244 259.0565 337.8824 442.5926 1.0000 2.1200 3.3744 4.7793 6.3528 8.1152 10.0890 12.2997 14.7757 17.5487 20.6546 24.1331 28.0291 32.3926 37.2797 42.7533 48.8837 55.7497 63.4397 72.0524 133.3339 241.3327 431.6635 767.0914 1.0000 2.1500 3.4725 4.9934 6.7424 8.7537 11.0668 13.7268 16.7858 20.3037 24.3493 29.0017 34.3519 40.5047 47.5804 55.7175 65.0751 75.8364 88.2118 102.4436 212.7930 434.7451 881.1702 1.779.0903 *Used to calculate the future value of a series of equal payments made at the end of each period. For example: What is the future value of $4.000 per year for 6 years assuming an annual interest rate of 8%? For (n=6, i = 8%), the FV factor is 7.3359. 54.000 per year for 6 years accumulates to $29.343.60 (54,000 7.3359)