Question

how long does it take a present value amount to triple if the expected return is 7%

Answer 1

Future value = Present Value ( 1 + r )^t where r is return and t is time

Assuming $1 is invested

3 x $1 = $1 ( 1 +0.07)^t

3 = (1 +0.07)^t

using the future value table we can see that @ 7% for 16 th year value of $1 will become 2.9522 . Hence it will take at least 16 years

FUTURE VALUE OF $1 RATE PER PERIOD 0.25% 0.50% 0.75% 1.00250 1.00500 1.00750 2 1.00501 1.01003 1.01506 | 1.00752 1.015081.02267 1.01004 1.02015 1.03034 | 1.01256 1.025251.03807 6 1.01509 1.03038 1.04585 7 1.01763 1.03553 1.05370 8 1.02018 | 1.04071 1.06160 1.02273 | 1.04591 1.06956 10 1.02528 1.05114 1.07758 1.05640 1.08566 12 1.030421.06168 1.09381 | 1.03299 1.06699 | 1.10201 | 1.03557 1.07232 1.11028 1.03816 1.07768 1.11860 16 1.04076 1.08307 1.12699 1.04336 1.08849 1.13544 1.04597 1.09393 1.14396 | 1.04858 1.09940 1.15254 20 | 1.05121 | 1.10490 1.16118 1.05383 1.11042 1.16989 1.05647 | 1.11597 1.17867 1.05911 1.12155 1.18751 1.06176 1.127161.19641 1.06441 1.132801.20539 | 1.07778 1.16140 1.25127 1.09132 1.19073 1.29890 1.10503 1.22079 | 1.34835 1.13297 1.28323 1.45296 1.00% 1.50% 2.00% 2.50% 3.00% 4.00% 5.00% 6.00% 7.00% 8.00% 9.00% 10.00% 11.00% 12.00% 1.01000 1.01500 1.02000 1.02500 1.03000 1.04000 1.05000 1.06000 1.07000 1.08000 1.09000 1.10000 1.11000 1.12000 1.02010 1.03023 1.04040 1.05063 | 1.06090 1.08160 1.10250 1.12360 1.14490 1.16640 1.18810 1.21000 1.23210 1.25440 1.03030 1.04568 1.06121 1.07689 1.09273 1.12486 1.15763 1.19102 1.225041.25971 1.295031.33100 1.36763 1.40493 1.04060 1.06136 1.08243 1.10381 1.12551 1.16986 1.21551 1.26248 1.31080 1.36049 1.41158 1.46410 1.51807 1.57352 1.05101 1.07728 1.10408 1.13141 1.15927 1.21665 1.27628 1.33823 1.40255 1.46933 1.53862 1.61051 1.68506 1.76234 1.06152 1.09344 1.126161.15969 1.19405 1.26532 1.34010 1.41852 1.50073 1.58687 1.67710 1.77156 1.87041 1.97382 1.07214 1.10984 1.14869 1.18869 1.22987 1.31593 1.40710 1.50363 1.60578 1.713821.82804 1.94872 2.07616 2.21068 1.08286 1.12649 1.17166 1.21840 1.26677 1.36857 1.47746 1.59385 1.71819 1.85093 1.99256 2.14359 2.30454 2.47596 1.09369 1.143391.19509 1.24886 1.30477 | 1.42331 1.551331.68948 1.83846 1.99900 2.17189 2.357952.55804 2.77308 1.10462 1.16054 1.21899 1.28008 1.34392 1.48024 1.62889 1.79085 1.96715 2.15892 2.36736 2.59374 2.839423.10585 1.11567 1.17795 1.24337 1.31209 1.38423 1.53945 1.71034 1.89830 2.10485 2.33164 2.580432 1.12683 1.19562 1.26824 1.344891.42576 1.60103 1.79586 2.01220 2.25219 2.51817 2.81266 3.13843 3.49845 3.89598 1.13809 | 1.21355 1.29361 1.37851 1.468531.66507 1.88565 2.13293 2.40985 2.71962 3.06580 3.452273.88328 4.36349 1.14947 1.23176 1.31948 1.41297 1.51259 1.73168 1.979932.26090 2.57853 2.93719 3.34173 3.79750 4.310444.88711 1.16097 1.25023 1.34587 1.44830 1.55797 1.80094 2.07893 2.39656 2.75903 3.172173.64248 4.17725 4.78459 5.47357 1.17258 1.26899 1.37279 1.48451 1.60471 1.87298 2.18287 2.54035 2.95216 3.42594 3.97031 4.59497 5.31089 6.13039 1.18430 1.28802 1.40024 1.521621.65285 1.94790 2.29202 2.69277 3.15882 3.70002 4.32763 5.05447 5.895096.86604 1.19615 1.30734 1.42825 1.55966 1.70243 2.02582 2.40662 2.85434 3.379933.99602 4.717125.55992 6.54355 7.68997 1.20811 1.32695 1.45681 1.59865 1.753512.10685 2.52695 3.02560 3.61653 4.31570 5.141666.11591 7.26334 8.61276 1.22019 1.34686 1.48595 1.63862 1.80611 2.19112 2.65330 3.20714 3.86968 4.66096 5.60441 6.72750 8.06231 9.64629 1.23239 1.36706 1.51567 1.67958 1.86029 2.27877 2.78596 3.39956 4.140565.03383 6.10881 7.40025 8.94917 10.80385 1.24472 1.38756 1.54598 1.72157 | 1.91610 2.36992 | 2.92526 3.60354 | 4.43040 5.43654 6.65860 8.14027 9.93357 12.10031 1.25716 1.40838 1.57690 1.76461 1.97359 2.46472 3.071523.81975 4.740535.87146 7.257878.95430 11.02627 13.55235 1.26973 1.42950 1.608441.80873 2.03279 2.56330 3.22510 4.04893 5.072376.34118 7.91108 9.84973 12.23916 15.17863 1.28243 1.45095 1.64061 1.85394 2.09378 2.66584 3.38635 4.29187 5.427436.84848 8.62308 10.83471 13.5854617.00006 1.34785 1.56308 1.81136 2.09757 2.42726 3.24340 4.321945.74349 7.61226 10.06266 13.26768 17.44940 22.89230 29.95992 1.41660 1.68388 1.99989 2.37321 2.81386 3.94609 5.51602 7.68609 10.67658 14.78534 20.41397 | 28.10244 38.5748552.79962| 1.48886 1.81402 2.20804 2.68506 3.26204 4.80102 7.03999 10.28572 14.97446 21.72452 31.40942 | 45.25926 65.00087 93.05097 1.64463 2.10524 2.69159 3.43711 4.38391 7.10668 11.46740 18.42015 29.45703 46.90161 74.35752 117.3909 184.5648 289.0022