Twins Natalie and Kaitlyn are both age 23. They both live in Warren, Ohio. Beginning at age 23, Natalie invests $3,000 per year for ten years and then never sets aside another penny. Kaitlyn waits ten years and then invests $3,000 per year for the next 30 years. Assume they both earn 7 percent. Round your answers to the nearest dollar. (Hint: Use Appendix A.1 and Appendix A.3 or visit the Garman/Forgue companion website.) Round Future value of a series of Equal Amounts and Future value of a Single Amount in intermediate calculations to four decimal places.

How much will Natalie have at age 63? $

How much will Kaitlyn have at age 63? $

 
 

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Appendix A-3 Future Value of a Series of Equal Amounts (an Annuity of $1 Paid at the End of Each Period) (Used to Compute the Compounded Future Value of a Stream of Income Payments) 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 1 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 2 2.0100 2.0200 2.0300 2.0400 2.0500 2.0500 2.0700 2.0800 2.0900 2.1000 2.1100 2.1200 2.1300 2.1400 2.1500 2.1600 2.1700 2.1800 2.1900 2.2000 3 3.0301 3.0604 3.0909 3.1216 3.1525 3.1836 3.2149 3.2464 3.2781 3.3100 3.3421 33744 3.4069 3.4396 3.4725 3.5056 3.5389 3.5724 3.6061 3.6400 4.0604 4.1216 4.1836 4.2465 43 101 4.3746 4.4399 4.5061 4.5731 4.64 10 4.7097 4.7793 4.8498 4.9211 4.9934 5.0665 5.1405 5.2154 5.2913 5.3680 5.1010 5.2040 5.3091 54163 5.5256 5.6371 5.7507 5.8666 5.9847 6. 1051 6.2278 63528 64803 6.6101 6.7424 6.8771 7.0144 7.1542 7.2966 7.44 16 6. 6.1520 6.3081 6.4684 6.6330 6.8019 6.9753 7.1533 7.3359 7.5233 7.7156 7.9129 8.1152 83227 8.5355 8.7537 8.9775 9.2068 9.4420 9.6830 9.9299 7 72135 74343 7.6625 7.8983 8.1420 8.3938 8.6540 8.9228 9.2004 9.4872 9.7833 10.0890 10.4047 10.7305 11.0668 11.4139 11.7720 12.1415 12.5227 12.9159 8 82857 B.5830 8.8923 9.2142 9.5491 9.8975 10.2598 10.6366 11.0285 11.4359 11.8594 12.2997 12.7573 13.2328 13.7268 14.2401 14.7733 15.3270 15.9020 16.4991 9 93685 9.7546 10.1591 10.5828 11.0 266 11.4913 11.9780 12.4876 13.02 10 13.5795 14.1640 14.7757 15.4157 16.0853 16.7858 17.5185 18.2847 19.0859 19.9234 20.7989 10 10 4622 10.9497 11.4639 12.0061 12.5779 13.1808 13.8164 14.4866 15. 1929 15.9374 16.72 20 17.5487 18.4197 19.3373 20.3037 21.3215 22.3931 23.5213 24.7089 25.9587 11 11.5668 12.1687 12.8078 134864 14.2068 14.9716 15.7836 16.6455 17.5603 18.5312 19.5614 20.6546 218143 23.0445 24.3493 25,7329 27.1999 28.7551 30 4035 32.1504 12 12.6825 13.4121 14.1920 15.0258 15.9171 16.8699 17.8885 18.9771 20.1407 21.3843 22.7132 24.1331 25.6502 27.2707 29.0017 30.8502 32.8239 34.9311 37.1802 39.5805 13 138093 14.6803 15.6178 16.6268 17.7130 18.8821 20.1406 21.4953 22.9534 24.5227 26.2116 28.0291 29.9847 32.0887 34.3519 36.7862 39.4040 42.2187 45.2445 48.4966 14 14.9474 15.9739 17.0863 18.2919 19.5986 21.0151 22.5505 24.2149 26.0192 27.9750 30.0949 32.3926 34.8827 37.5811 40.5047 43.6720 47.1027 50.8 180 54 8409 59.1959 15 16.0969 17.2934 18.5989 20.0236 21.5786 23.2760 25.1290 27.1521 29.3609 31.7725 34.4054 37.2797 404175 43.8424 47.5804 51.6595 56.1101 60.9653 66.2607 72.0351 16 17.2579 18,6393 20.1569 21.8245 236575 25.6725 27 8881 30.3243 33.0034 35.9497 39. 1899 42.7533 46.6717 50.9804 55.7175 60.9250 66.6488 72.9390 798502 87.4421 17 18.4304 20.0121 21.7616 23.6975 25.8404 28.2129 308402 33.7502 36.9737 40.5447 44.5008 48.8837 53.7391 59.1176 65.0751 71.6730 78.9791 87.0680 96.0217 105.9306 18 19.6147 21.4123 23.4144 25.6454 28.1324 30.9057 33.9990 37.4502 41.3013 45.5992 50.3959 55.7497 61.7251 68.3941 75.8364 84.1407 93.4056 103.7403 115.2659 128.1167 19 208 109 22.8406 25.1169 27.6712 30.5390 33.7600 37.3790 41.4463 46.0185 51.1591 56.9395 63.4397 70.7494 78.9692 88.2118 98.6032 110 2846 123.4135 138.1664 154.7400 20 220190 24.2974 26.8704 29.7781 33.0660 36.7856 40.9955 45.7620 51. 1601 57.2750 64.2028 72.0524 80.9468 91.0249 102.4436 115.3797 130.0329 146.6280 165.4180 186.6880 21 23 2392 25.7833 28.6765 31.9692 35.7193 39.9927 44.8552 50.4229 56.7645 64.0025 72.2651 81.6987 92.4699 104.7684 118.8101 134.8405 153.1385 174.0210 197.8474 225.0256 22 244716 27.2990 30.5368 34.2480 38.5052 43.3923 49.0057 55.4568 62.8733 71.4027 81.2143 92.5026 105.4910 120.4360 137.63 16 157.4150 180.1721 206.3448 236.4384 271.0307 23 25.7163 28.8450 32.4529 36.6179 41.4305 46.9958 53.4361 60.8933 69.53 19 79.5430 91.1479 104.6029 120.2048 138.2970 159.2764 183.6014 211.8013 244.4868 282.3618 326.2368 24 26.9735 30.4219 34.4265 39.0826 44.5020 50.8156 58.1767 66.7648 76.7898 88.4973 102.1741 118.1552 136.8315 158.6586 184. 1678 213.9776 248.8075 289.4945 337.0 105 392.4842 25 282432 32.0303 364593 41.6459 47.7271 54,8645 63.2490 73. 1059 84.7009 98.3471 1144133 133.3339 155.6196 181.8708 212.7930 249.2140 292,1048 342.6035 402.0424 471.9811 26 29.5256 33.6709 38.5530 44.3117 51.1135 59.1564 68.6765 79.9544 93.3240 109. 1818 127.9988 150.3339 176.8501 208.3327 245.7120 290.0883 342.7626 405.2721 4794305 567.3773 27 308209 353443 40.7096 47.0842 54.6691 63.7058 74.4838 87.3508 102.7231 121.0999 143.0786 1693740 200B406 238.4993 283.5688 337.5024 402.0323 479.2211 571.5223 681.8527 28 32.1291 37.0512 42.9309 49.9676 58.4026 68.5281 80.6977 95.3388 112.9682 134.2099 159.8173 190.6989 227.9499 272.8892 327.1041 392.5027 471.3778 566.4808 681.1116 819.2233 29 334504 38.7922 45.2188 52.9663 62.3227 73.6398 87.3465 103.9659 124.1354 148.6309 178.3972 214.5827 258.5834 312.0937 377.1697 456.3032 552.5120 669.4474 811.5228 984.0679 30 34.7849 40.5681 47.5754 56.0849 664389 79.0582 94.4608 113.2832 136.3075 164.4940 199.0209 241.3327 293.1992 356.7868 434.7451 530.3117 647,4390 790.9479 966.7121 1181.882 40 48 8864 60.4020 75.4013 95.0255 120.7998 154.7620 199.6351 259.0565 337,8824 442.5925 581.8260 767.0914 1013.704 1342.025 1779.090 2360,757 3134.522 4163.212 5529829 7343.856 50 64 4632 84.5794 112.7969 152.6671 209.3480 290.3359 405.5289 573.7701 815.0834 1163.908 1668.771 2400.018 3459.507 4994.522 7217.714 10435.65 15089.50 21813.09 31515.33 45497.17 Appendix A-3 Future Value of a Series of Equal Amounts (an Annuity of $1 Paid at the End of Each Period) (Used to Compute the Compounded Future Value of a Stream of Income Payments) 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 1 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 2 2.0100 2.0200 2.0300 2.0400 2.0500 2.0500 2.0700 2.0800 2.0900 2.1000 2.1100 2.1200 2.1300 2.1400 2.1500 2.1600 2.1700 2.1800 2.1900 2.2000 3 3.0301 3.0604 3.0909 3.1216 3.1525 3.1836 3.2149 3.2464 3.2781 3.3100 3.3421 33744 3.4069 3.4396 3.4725 3.5056 3.5389 3.5724 3.6061 3.6400 4.0604 4.1216 4.1836 4.2465 43 101 4.3746 4.4399 4.5061 4.5731 4.64 10 4.7097 4.7793 4.8498 4.9211 4.9934 5.0665 5.1405 5.2154 5.2913 5.3680 5.1010 5.2040 5.3091 54163 5.5256 5.6371 5.7507 5.8666 5.9847 6. 1051 6.2278 63528 64803 6.6101 6.7424 6.8771 7.0144 7.1542 7.2966 7.44 16 6. 6.1520 6.3081 6.4684 6.6330 6.8019 6.9753 7.1533 7.3359 7.5233 7.7156 7.9129 8.1152 83227 8.5355 8.7537 8.9775 9.2068 9.4420 9.6830 9.9299 7 72135 74343 7.6625 7.8983 8.1420 8.3938 8.6540 8.9228 9.2004 9.4872 9.7833 10.0890 10.4047 10.7305 11.0668 11.4139 11.7720 12.1415 12.5227 12.9159 8 82857 B.5830 8.8923 9.2142 9.5491 9.8975 10.2598 10.6366 11.0285 11.4359 11.8594 12.2997 12.7573 13.2328 13.7268 14.2401 14.7733 15.3270 15.9020 16.4991 9 93685 9.7546 10.1591 10.5828 11.0 266 11.4913 11.9780 12.4876 13.02 10 13.5795 14.1640 14.7757 15.4157 16.0853 16.7858 17.5185 18.2847 19.0859 19.9234 20.7989 10 10 4622 10.9497 11.4639 12.0061 12.5779 13.1808 13.8164 14.4866 15. 1929 15.9374 16.72 20 17.5487 18.4197 19.3373 20.3037 21.3215 22.3931 23.5213 24.7089 25.9587 11 11.5668 12.1687 12.8078 134864 14.2068 14.9716 15.7836 16.6455 17.5603 18.5312 19.5614 20.6546 218143 23.0445 24.3493 25,7329 27.1999 28.7551 30 4035 32.1504 12 12.6825 13.4121 14.1920 15.0258 15.9171 16.8699 17.8885 18.9771 20.1407 21.3843 22.7132 24.1331 25.6502 27.2707 29.0017 30.8502 32.8239 34.9311 37.1802 39.5805 13 138093 14.6803 15.6178 16.6268 17.7130 18.8821 20.1406 21.4953 22.9534 24.5227 26.2116 28.0291 29.9847 32.0887 34.3519 36.7862 39.4040 42.2187 45.2445 48.4966 14 14.9474 15.9739 17.0863 18.2919 19.5986 21.0151 22.5505 24.2149 26.0192 27.9750 30.0949 32.3926 34.8827 37.5811 40.5047 43.6720 47.1027 50.8 180 54 8409 59.1959 15 16.0969 17.2934 18.5989 20.0236 21.5786 23.2760 25.1290 27.1521 29.3609 31.7725 34.4054 37.2797 404175 43.8424 47.5804 51.6595 56.1101 60.9653 66.2607 72.0351 16 17.2579 18,6393 20.1569 21.8245 236575 25.6725 27 8881 30.3243 33.0034 35.9497 39. 1899 42.7533 46.6717 50.9804 55.7175 60.9250 66.6488 72.9390 798502 87.4421 17 18.4304 20.0121 21.7616 23.6975 25.8404 28.2129 308402 33.7502 36.9737 40.5447 44.5008 48.8837 53.7391 59.1176 65.0751 71.6730 78.9791 87.0680 96.0217 105.9306 18 19.6147 21.4123 23.4144 25.6454 28.1324 30.9057 33.9990 37.4502 41.3013 45.5992 50.3959 55.7497 61.7251 68.3941 75.8364 84.1407 93.4056 103.7403 115.2659 128.1167 19 208 109 22.8406 25.1169 27.6712 30.5390 33.7600 37.3790 41.4463 46.0185 51.1591 56.9395 63.4397 70.7494 78.9692 88.2118 98.6032 110 2846 123.4135 138.1664 154.7400 20 220190 24.2974 26.8704 29.7781 33.0660 36.7856 40.9955 45.7620 51. 1601 57.2750 64.2028 72.0524 80.9468 91.0249 102.4436 115.3797 130.0329 146.6280 165.4180 186.6880 21 23 2392 25.7833 28.6765 31.9692 35.7193 39.9927 44.8552 50.4229 56.7645 64.0025 72.2651 81.6987 92.4699 104.7684 118.8101 134.8405 153.1385 174.0210 197.8474 225.0256 22 244716 27.2990 30.5368 34.2480 38.5052 43.3923 49.0057 55.4568 62.8733 71.4027 81.2143 92.5026 105.4910 120.4360 137.63 16 157.4150 180.1721 206.3448 236.4384 271.0307 23 25.7163 28.8450 32.4529 36.6179 41.4305 46.9958 53.4361 60.8933 69.53 19 79.5430 91.1479 104.6029 120.2048 138.2970 159.2764 183.6014 211.8013 244.4868 282.3618 326.2368 24 26.9735 30.4219 34.4265 39.0826 44.5020 50.8156 58.1767 66.7648 76.7898 88.4973 102.1741 118.1552 136.8315 158.6586 184. 1678 213.9776 248.8075 289.4945 337.0 105 392.4842 25 282432 32.0303 364593 41.6459 47.7271 54,8645 63.2490 73. 1059 84.7009 98.3471 1144133 133.3339 155.6196 181.8708 212.7930 249.2140 292,1048 342.6035 402.0424 471.9811 26 29.5256 33.6709 38.5530 44.3117 51.1135 59.1564 68.6765 79.9544 93.3240 109. 1818 127.9988 150.3339 176.8501 208.3327 245.7120 290.0883 342.7626 405.2721 4794305 567.3773 27 308209 353443 40.7096 47.0842 54.6691 63.7058 74.4838 87.3508 102.7231 121.0999 143.0786 1693740 200B406 238.4993 283.5688 337.5024 402.0323 479.2211 571.5223 681.8527 28 32.1291 37.0512 42.9309 49.9676 58.4026 68.5281 80.6977 95.3388 112.9682 134.2099 159.8173 190.6989 227.9499 272.8892 327.1041 392.5027 471.3778 566.4808 681.1116 819.2233 29 334504 38.7922 45.2188 52.9663 62.3227 73.6398 87.3465 103.9659 124.1354 148.6309 178.3972 214.5827 258.5834 312.0937 377.1697 456.3032 552.5120 669.4474 811.5228 984.0679 30 34.7849 40.5681 47.5754 56.0849 664389 79.0582 94.4608 113.2832 136.3075 164.4940 199.0209 241.3327 293.1992 356.7868 434.7451 530.3117 647,4390 790.9479 966.7121 1181.882 40 48 8864 60.4020 75.4013 95.0255 120.7998 154.7620 199.6351 259.0565 337,8824 442.5925 581.8260 767.0914 1013.704 1342.025 1779.090 2360,757 3134.522 4163.212 5529829 7343.856 50 64 4632 84.5794 112.7969 152.6671 209.3480 290.3359 405.5289 573.7701 815.0834 1163.908 1668.771 2400.018 3459.507 4994.522 7217.714 10435.65 15089.50 21813.09 31515.33 45497.17