Table 1. Discount factors.
The present value of I received or spent in a given future year 'n' at a given discount 'i'.
Discount factor: 1/(1 + i)n
|
% |
2 |
4 |
5 |
6 |
8 |
9 |
10 |
12 |
14 |
15 |
16 |
18 |
20 |
25 |
30 |
35 |
40 |
45 |
50 |
|
Yrs |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
.980 |
.962 |
.952 |
.943 |
.926 |
.917 |
.909 |
.893 |
.877 |
.870 |
.862 |
.847 |
.833 |
.800 |
.769 |
.741 |
.714 |
.690 |
,667 |
|
2 |
.961 |
.925 |
.907 |
.890 |
.857 |
.842 |
.826 |
.797 |
.769 |
.756 |
.743 |
.718 |
.694 |
.640 |
.592 |
.549 |
.510 |
.476 |
.444 |
|
3 |
.942 |
.889 |
.864 |
.840 |
.794 |
.772 |
.751 |
.712 |
.675 |
.658 |
.641 |
.609 |
.579 |
.512 |
.455 |
.406 |
.364 |
.328 |
.296 |
|
4 |
.924 |
.855 |
.823 |
.792 |
.735 |
.708 |
.683 |
.636 |
.592 |
.572 |
.552 |
.516 |
.482 |
.410 |
.350 |
.301 |
.260 |
.226 |
.198 |
|
5 |
.906 |
.822 |
.784 |
.747 |
.681 |
.650 |
.621 |
.567 |
.519 |
.497 |
.476 |
.437 |
.402 |
.328 |
.269 |
.223 |
.186 |
.156 |
.132 |
|
6 |
.888 |
.790 |
.746 |
.705 |
.630 |
.596 |
.564 |
.507 |
.456 |
.432 |
.410 |
.370 |
.335 |
.262 |
.207 |
.165 |
.133 |
.108 |
.088 |
|
7 |
.871 |
.760 |
.711 |
.665 |
.583 |
.547 |
.513 |
.452 |
.400 |
.376 |
.354 |
.314 |
.279 |
.210 |
.159 |
.122 |
.095 |
.074 |
.059 |
|
8 |
.853 |
.731 |
.677 |
.627 |
.540 |
.502 |
.467 |
.404 |
.351 |
.327 |
.305 |
.266 |
.233 |
.168 |
.123 |
.091 |
.068 |
.051 |
.039 |
|
9 |
.837 |
.703 |
.645 |
.592 |
.500 |
.460 |
.424 |
.361 |
.308 |
.284 |
.263 |
.225 |
.194 |
.134 |
.094 |
.067 |
.048 |
.035 |
.026 |
|
10 |
.820 |
.676 |
.614 |
.558 |
.463 |
.422 |
.386 |
.322 |
.270 |
.247 |
.227 |
.191 |
.162 |
.107 |
.073 |
.050 |
.035 |
.024 |
.017 |
|
11 |
.804 |
.650 |
.585 |
.527 |
.429 |
.388 |
.350 |
.287 |
.237 |
.215 |
.195 |
.162 |
.135 |
.086 |
.056 |
.037 |
.025 |
.017 |
.012 |
|
12 |
.788 |
.625 |
.557 |
.497 |
.397 |
.356 |
.319 |
.257 |
.208 |
.187 |
.168 |
.137 |
.112 |
.069 |
.043 |
.027 |
.018 |
.012 |
.008 |
|
13 |
.773 |
.601 |
.530 |
.469 |
.368 |
.326 |
.290 |
.229 |
.182 |
.163 |
.145 |
.116 |
.093 |
.055 |
.033 |
.020 |
.013 |
.008 |
.005 |
|
14 |
.758 |
.577 |
.505 |
.442 |
.340 |
.299 |
.263 |
.205 |
.160 |
.141 |
.125 |
.099 |
.078 |
.044 |
.025 |
.015 |
.009 |
.006 |
.003 |
|
15 |
.743 |
.555 |
.481 |
.417 |
.315 |
.275 |
.239 |
.183 |
.140 |
.123 |
.108 |
.084 |
.065 |
.035 |
.020 |
.011 |
.006 |
.004 |
.002 |
|
16 |
.728 |
.534 |
.458 |
.394 |
.292 |
.252 |
.218 |
.163 |
.123 |
.107 |
.093 |
.071 |
.054 |
.028 |
.015 |
.008 |
.005 |
.003 |
.002 |
|
17 |
.714 |
.513 |
.436 |
.371 |
.270 |
.231 |
.198 |
.146 |
.108 |
.093 |
.080 |
.060 |
.045 |
.023 |
.012 |
.006 |
.003 |
.002 |
.001 |
|
18 |
.700 |
.494 |
.416 |
.350 |
.250 |
.212 |
.180 |
.130 |
.095 |
.081 |
.069 |
.051 |
.038 |
.018 |
.009 |
.005 |
.002 |
.001 |
.001 |
|
19 |
.686 |
.475 |
.396 |
.331 |
.232 |
.194 |
.164 |
.116 |
.083 |
.070 |
.060 |
.043 |
.031 |
.014 |
.007 |
.003 |
.002 |
.001 |
.000 |
|
20 |
.673 |
.456 |
.377 |
.312 |
.215 |
.178 |
.149 |
.104 |
.073 |
.061 |
.051 |
.037 |
.026 |
.012 |
.005 |
.002 |
.001 |
.001 |
.000 |
|
21 |
.660 |
.439 |
.359 |
.294 |
.199 |
.164 |
.135 |
.093 |
.064 |
.053 |
.044 |
.031 |
.022 |
.009 |
.004 |
.002 |
.001 |
.000 |
.000 |
|
22 |
.647 |
.422 |
342 |
.278 |
.184 |
.150 |
.123 |
.083 |
.056 |
.046 |
.038 |
.026 |
.018 |
.007 |
.003 |
.001 |
.001 |
.000 |
.000 |
|
23 |
.634 |
.406 |
.326 |
.262 |
.170 |
.138 |
.112 |
.074 |
.049 |
.040 |
.033 |
.022 |
.015 |
.006 |
.002 |
.001 |
.000 |
.000 |
.000 |
|
24 |
.622 |
.390 |
.310 |
.247 |
.158 |
.126 |
.102 |
.066 |
.043 |
.035 |
.028 |
.019 |
.013 |
.005 |
.002 |
.001 |
.000 |
.000 |
.000 |
|
25 |
.610 |
.375 |
.295 |
.233 |
.146 |
.116 |
.092 |
.059 |
.038 |
.030 |
.024 |
.016 |
.010 |
.004 |
.001 |
.001 |
.000 |
.000 |
.000 |
|
30 |
.552 |
.308 |
.231 |
.174 |
.099 |
.075 |
.057 |
.033 |
.020 |
.015 |
.012 |
.007 |
.004 |
.001 |
.000 |
.000 |
.000 |
.000 |
.000 |
|
35 |
.500 |
.253 |
.181 |
.130 |
.068 |
.049 |
.036 |
.019 |
.010 |
.008 |
.006 |
.003 |
.002 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
|
40 |
.453 |
.208 |
.142 |
.097 |
.046 |
.032 |
.022 |
.011 |
.005 |
.004 |
.003 |
.001 |
.001 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
|
45 |
.410 |
.171 |
.111 |
.073 |
.031 |
.021 |
.014 |
.006 |
.003 |
.002 |
.001 |
.001 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
|
50 |
.372 |
.141 |
.087 |
.054 |
.021 |
.013 |
.009 |
.003 |
.001 |
.001 |
.001 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
Table 2. Present value of an annuity.
The present value of I received or spent annually at a given rate of interest 'i' for a given number of years 'n'.
Present value of an annuity factor: S 1/(1 + i)n
|
% |
2 |
4 |
5 |
6 |
8 |
9 |
10 |
12 |
14 |
15 |
16 |
18 |
20 |
25 |
30 |
35 |
40 |
50 |
|
Yrs |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
.9804 |
.9615 |
.9524 |
.9434 |
.9259 |
.9174 |
.9091 |
.8929 |
.8772 |
.8696 |
.8621 |
.8475 |
.8333 |
.8000 |
.7692 |
.7407 |
.7143 |
.6667 |
|
2 |
1.942 |
1.886 |
1.859 |
1.833 |
1.783 |
1.759 |
1.736 |
1.690 |
1.647 |
1.626 |
1.605 |
1.566 |
1.528 |
1.440 |
1.361 |
1.289 |
1.224 |
1.111 |
|
3 |
2.884 |
2.775 |
2.723 |
2.673 |
2.577 |
2.531 |
2.487 |
2.402 |
2.322 |
2.283 |
2.246 |
2.174 |
2.106 |
1.952 |
1.816 |
1.696 |
1.589 |
1.407 |
|
4 |
3.808 |
3.630 |
3.546 |
3.465 |
3.312 |
3.240 |
3.170 |
3.037 |
2.914 |
2.855 |
2.798 |
2.690 |
2.589 |
2.362 |
2.166 |
1.997 |
1.849 |
1.605 |
|
5 |
4.713 |
4.452 |
4.329 |
4.212 |
3.993 |
3.890 |
3.791 |
3.605 |
3.433 |
3.352 |
3.274 |
3,127 |
2.991 |
2.689 |
2.436 |
2.220 |
2.035 |
1.737 |
|
6 |
5.601 |
5.242 |
5.076 |
4.917 |
4.623 |
4.486 |
4.355 |
4.111 |
3.889 |
3.784 |
3.685 |
3.498 |
3.326 |
2.951 |
2.643 |
2.385 |
2.168 |
1.824 |
|
7 |
6.472 |
6.002 |
5.786 |
5.582 |
5.206 |
5.033 |
4.868 |
4.564 |
4.288 |
4.160 |
4.039 |
3.812 |
3.605 |
3.161 |
2.802 |
2.508 |
2.263 |
1.883 |
|
8 |
7.325 |
6.733 |
6.463 |
6.210 |
5.747 |
5.535 |
5.335 |
4.968 |
4.639 |
4.487 |
4.344 |
4.078 |
3.837 |
3.329 |
2.925 |
2.598 |
2.331 |
1.922 |
|
9 |
8.162 |
7.435 |
7.108 |
6.802 |
6.247 |
5.995 |
5.759 |
5.328 |
4.946 |
4.772 |
4.607 |
4.303 |
4.031 |
3.463 |
3.019 |
2.665 |
2.379 |
1.948 |
|
10 |
8.983 |
8.111 |
7.722 |
7.360 |
6.710 |
6.418 |
6.145 |
5.650 |
5.216 |
5.019 |
4.833 |
4.494 |
4.192 |
3.571 |
3.092 |
2.715 |
2.414 |
1.965 |
|
11 |
9.787 |
8.760 |
8.306 |
7.887 |
7.139 |
6.805 |
6.495 |
5.938 |
5.453 |
5.234 |
5.029 |
4.656 |
4.327 |
3.656 |
3.147 |
2.752 |
2.438 |
1.977 |
|
12 |
10.58 |
9.385 |
8.863 |
8.384 |
7.536 |
7.161 |
6.814 |
6.194 |
5.660 |
5.421 |
5.197 |
4.793 |
4.439 |
3.725 |
3.190 |
2.779 |
2.456 |
1.985 |
|
13 |
11.35 |
9.986 |
9.394 |
8.853 |
7.904 |
7.487 |
7.103 |
6.424 |
5.842 |
5.583 |
5.342 |
4.910 |
4.533 |
3.780 |
3.223 |
2.799 |
2.469 |
1.990 |
|
14 |
12.11 |
10.56 |
9.899 |
9.295 |
8.244 |
7.786 |
7.367 |
6.628 |
6.002 |
5.724 |
5.468 |
5.008 |
4.611 |
3.824 |
3.249 |
2.814 |
2.478 |
1.993 |
|
15 |
12.85 |
11.12 |
10.38 |
9.712 |
8.559 |
8.061 |
7.606 |
6.811 |
6.142 |
5.847 |
5.575 |
5.092 |
4.675 |
3.859 |
3.268 |
2.825 |
2.484 |
1.995 |
|
16 |
13.58 |
11.65 |
10.84 |
10.11 |
8.851 |
8.313 |
7.824 |
6.974 |
6.265 |
5.954 |
5.668 |
5.162 |
4.730 |
3.887 |
3.283 |
2.834 |
2.489 |
1.997 |
|
17 |
14.29 |
12.17 |
11.27 |
10.48 |
9.122 |
8.544 |
8.022 |
7.120 |
6.373 |
6.047 |
5.749 |
5.222 |
4.77 |
3.910 |
3.295 |
2.840 |
2.492 |
1.998 |
|
18 |
14.99 |
12.66 |
11.69 |
10.83 |
9.372 |
8.756 |
8.201 |
7.250 |
6.467 |
6.128 |
5.818 |
5.273 |
4.813 |
3.928 |
3.304 |
2.844 |
2.494 |
1.999 |
|
19 |
15.68 |
13.13 |
12.09 |
11.16 |
9.604 |
8.950 |
8.365 |
71366 |
6.550 |
6.198 |
5.877 |
5.316 |
4.843 |
3.942 |
3.311 |
2.848 |
2.496 |
1.999 |
|
20 |
16.35 |
13.59 |
12.46 |
11.47 |
9.818 |
9.129 |
8.514 |
7.469 |
6.623 |
6.259 |
5.929 |
5.353 |
4.870 |
3.954 |
3.316 |
2.850 |
2.497 |
1.999 |
|
21 |
17.01 |
14.03 |
12.82 |
11.76 |
10.02 |
9.292 |
8.649 |
7.562 |
6.687 |
6.312 |
5.973 |
5.384 |
4.891 |
3.963 |
3.320 |
2.852 |
2.498 |
2.000 |
|
22 |
17.66 |
14.45 |
13.16 |
12.04 |
10.20 |
9.442 |
8.772 |
7.645 |
6.743 |
6.359 |
6.011 |
5.410 |
4.909 |
3.970 |
3.323 |
2.853 |
2.498 |
2.000 |
|
23 |
18.29 |
14.86 |
13.49 |
12'30 |
10.37 |
9.580 |
8.883 |
7.718 |
6.792 |
6.399 |
6.044 |
5.432 |
4.925 |
3.976 |
3.325 |
2.854 |
2.499 |
2.000 |
|
24 |
18.91 |
15.25 |
13.80 |
12.55 |
10.53 |
9.707 |
8.985 |
7.784 |
6.835 |
6.434 |
6.073 |
5.451 |
4.937 |
3.981 |
3.327 |
2.855 |
2.499 |
2.000 |
|
25 |
19.52 |
15.62 |
14.09 |
12.78 |
10.67 |
9.823 |
9.077 |
7.843 |
6.873 |
6.464 |
6.097 |
5.467 |
4.948 |
3.985 |
3.329 |
2.856 |
2.499 |
2.000 |
|
30 |
22.40 |
17.29 |
15.37 |
13.76 |
11.26 |
10.27 |
9.427 |
8.055 |
7.003 |
6.566 |
6.177 |
5.517 |
4.979 |
3.995 |
3.332 |
2.857 |
2.500 |
2.000 |
|
35 |
25.00 |
18.66 |
16.37 |
14.50 |
11.65 |
10.57 |
9.644 |
8.176 |
7.070 |
6.617 |
6.215 |
5.539 |
4.992 |
3.998 |
3.333 |
2.857 |
2.500 |
2.000 |
|
40 |
27.36 |
19.79 |
17.16 |
15.05 |
11.92 |
10.76 |
9.779 |
8.244 |
7.105 |
6.642 |
6.233 |
5.548 |
4.997 |
3.999 |
3.333 |
2.857 |
2.500 |
2.000 |
|
45 |
29.49 |
20.72 |
17.77 |
15.46 |
12.11 |
10.88 |
9.863 |
8.283 |
7.123 |
6.654 |
6.242 |
5.552 |
4.999 |
4.000 |
3.333 |
2.857 |
2.500 |
2.000 |
|
50 |
31.42 |
21.48 |
18.26 |
15.76 |
12.23 |
10.96 |
9.915 |
8.304 |
7.133 |
6.661 |
6.246 |
5.554 |
4.999 |
4.000 |
3.333 |
2.857 |
2.500 |
2.000 |
Table 3. Compound interest factors.
The future value of I invested at a given rate of interest 'i' for a given number of years 'n'.
Compounding factor: 1 x (1 + i)n
|
% |
2 |
4 |
5 |
6 |
8 |
9 |
10 |
12 |
14 |
15 |
16 |
18 |
20 |
25 |
30 |
35 |
40 |
45 |
50 |
|
Yrs |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
1.020 |
1.040 |
1.050 |
1.060 |
1.080 |
1.090 |
1.100 |
1.120 |
1.140 |
1.150 |
1.160 |
.1.180 |
1.200 |
1.250 |
1.300 |
1.350 |
1.400 |
1.450 |
1.500 |
|
2 |
1.040 |
1.082 |
1.103 |
1.124 |
1.166 |
1.188 |
1.210 |
1.254 |
1.300 |
1.323 |
1.346 |
1.392 |
1.440 |
1.563 |
1.690 |
1.823 |
1.960 |
2.103 |
2.250 |
|
3 |
1.061 |
1.125 |
1.158 |
1.191 |
1.260 |
1.295 |
1.331 |
1.405 |
1.482 |
1.521 |
1.561 |
1.643 |
1.728 |
1.953 |
2.197 |
2.460 |
2.744 |
3.049 |
3.375 |
|
4 |
1.082 |
1.170 |
1.216 |
1.262 |
1.360 |
1.412 |
1.464 |
1.574 |
1.689 |
1.749 |
1.811 |
1.939 |
2.074 |
2.441 |
2.856 |
3.322 |
3.842 |
4.421 |
5.063 |
|
5 |
1.104 |
1.217 |
1.276 |
1.338 |
1.469 |
1.539 |
1.611 |
1.762 |
1.925 |
2.011 |
2.100 |
2.288 |
2.488 |
3.052 |
3.713 |
4.484 |
5.378 |
6.410 |
7.594 |
|
6 |
1.126 |
1.265 |
1.340 |
1.419 |
1.587 |
1.677 |
1.772 |
1.974 |
2.195 |
2.313 |
2.436 |
2.700 |
2.986 |
3.815 |
4.827 |
6.053 |
7.530 |
9.294 |
11.39 |
|
7 |
1.149 |
1.316 |
1.407 |
1.504 |
1.714 |
1.828 |
1.949 |
2.211 |
2.502 |
2.660 |
2.826 |
3.185 |
3.583 |
4.768 |
6.275 |
8.172 |
10.54 |
13.48 |
17.09 |
|
8 |
1.172 |
1.369 |
1.477 |
1.594 |
1.851 |
1.993 |
2.144 |
2.476 |
2.853 |
3.059 |
3.278 |
3.759 |
4.300 |
5.960 |
8.157 |
11.03 |
14.76 |
19.54 |
25.63 |
|
9 |
1.195 |
1.423 |
1.551 |
1.689 |
1.999 |
2.172 |
2.358 |
2.773 |
3.252 |
3.518 |
3.803 |
4.435 |
5.160 |
7.451 |
10.60 |
14.89 |
20.66 |
28.33 |
38.44 |
|
10 |
1.219 |
1.480 |
1.629 |
1.791 |
2.159 |
2.367 |
2.594 |
3.106 |
3.707 |
4.046 |
4.411 |
5.234 |
6.192 |
9.313 |
13.79 |
20.11 |
28.93 |
41.08 |
57.67 |
|
11 |
1.243 |
1.539 |
1.710 |
1.898 |
2.332 |
2.580 |
2.853 |
3.479 |
4.226 |
4.652 |
5.117 |
6.176 |
7.430 |
11.64 |
17.92 |
27.14 |
40.50 |
59.57 |
86.50 |
|
12 |
1.268 |
1.601 |
1.796 |
2.012 |
2.518 |
2.813 |
3.138 |
3.896 |
4.818 |
5.350 |
5.936 |
7.288 |
8.916 |
14.55 |
23.30 |
36.64 |
56.69 |
86.38 |
129.7 |
|
13 |
1.294 |
1.665 |
1.886 |
2.133 |
2.720 |
3.066 |
3.452 |
4.363 |
5.492 |
6.153 |
6.886 |
8.599 |
10.70 |
18.19 |
30.29 |
49.47 |
79.37 |
125.3 |
194.6 |
|
14 |
1.319 |
1.732 |
1.980 |
2.261 |
2.937 |
3.342 |
3.797 |
4.887 |
6.261 |
7.076 |
7.988 |
10.15 |
12.84 |
22.74 |
39.37 |
66.78 |
111.1 |
181.6 |
291.9 |
|
15 |
1.346 |
1.801 |
2.079 |
2.397 |
3.172 |
3.642 |
4.177 |
5.474 |
7.138 |
8.137 |
9.266 |
11.97 |
15.41 |
28.42 |
51.19 |
90.16 |
155.6 |
263.3 |
437.9 |
|
16 |
1.373 |
1.873 |
2.183 |
2.540 |
3.426 |
3.970 |
4.595 |
6.130 |
8.137 |
9.358 |
10.75 |
14.13 |
18.49 |
35.53 |
66.54 |
121.7 |
217.8 |
381.8 |
656.8 |
|
17 |
1.400 |
1.948 |
2.292 |
2.693 |
3.700 |
4.328 |
5.054 |
6.866 |
9.276 |
10.76 |
12.47 |
16.67 |
22.19 |
44.41 |
86.50 |
164.3 |
304.9 |
553.7 |
985.3 |
|
18 |
1.428 |
2.026 |
2.407 |
2.854 |
3.996 |
4.717 |
5.560 |
7.690 |
10.58 |
12.38 |
14.46 |
19.67 |
26.62 |
55.51 |
112.5 |
221.8 |
426.9 |
802.8 |
1478. |
|
19 |
1.457 |
2.107 |
2.527 |
3.026 |
4.316 |
5.142 |
6.116 |
8.613 |
12.06 |
14.23 |
16.78 |
23.21 |
31.95 |
69.39 |
146.2 |
299.5 |
597.6 |
1164. |
2217. |
|
20 |
1.486 |
2.191 |
2.653 |
3.207 |
4.661 |
5.604 |
6.727 |
9.646 |
13.74 |
16.37 |
19.46 |
27.39 |
38.34 |
86.74 |
190.0 |
404.3 |
836.7 |
1688. |
3325. |
|
21 |
1.516 |
2.279 |
2.786 |
3.400 |
5.034 |
6.109 |
7.400 |
10.80 |
15.67 |
18.82 |
22.57 |
32.32 |
46.01 |
108.4 |
247.1 |
545.8 |
1171. |
2448. |
4988. |
|
22 |
1.546 |
2.370 |
2.925 |
3.604 |
5.437 |
6.659 |
8.140 |
12.10 |
17,86 |
21.64 |
26.19 |
38.14 |
55.21 |
135.5 |
321.2 |
736.8 |
1640. |
3549. |
7482. |
|
23 |
1.577 |
2.465 |
3.072 |
3.820 |
5.871 |
7.258 |
8.954 |
13.55 |
20.36 |
24.89 |
30.38 |
45.01 |
66.25 |
169.4 |
417.5 |
994.7 |
2296. |
5146. |
11223 |
|
24 |
1.608 |
2.563 |
3.225 |
4.049 |
6.341 |
7.911 |
9.850 |
15.18 |
23.21 |
28.63 |
35.24 |
53.11 |
79.50 |
211.8 |
542.8 |
1343. |
3214. |
7462. |
16834 |
|
25 |
1.641 |
2.666 |
3.386 |
4.292 |
6.848 |
8.623 |
10.83 |
17.00 |
26.46 |
32.92 |
40.87 |
62.67 |
95.40 |
264.7 |
705.6 |
1813. |
4500. |
10819 |
25251 |
|
30 |
1.811 |
3.243 |
4.322 |
5.743 |
10.06 |
13.27 |
17.45 |
29.96 |
50.95 |
66.21 |
85.85 |
143.4 |
237.4 |
807.8 |
2620. |
8129. |
24210 |
69349 |
>100t |
|
35 |
2.000 |
3.946 |
5.516 |
7.686 |
14.79 |
20.41 |
28.10 |
52.80 |
98.10 |
133.2 |
180.3 |
328.0 |
590.7 |
2465. |
9728. |
36449 |
>100t |
>100t |
>100t |
|
40 |
2.208 |
4.801 |
7.040 |
10.29 |
21.72 |
31.41 |
45.26 |
93.05 |
188.9 |
267.9 |
378.7 |
750.4 |
1470. |
7523. |
36119 |
>100t |
>100t |
>100t |
>100t |
|
45 |
2.438 |
5.841 |
8.985 |
13.76 |
31.92 |
48.33 |
72.89 |
164.0 |
363.7 |
538.8 |
795.4 |
1717. |
3657. |
22959 |
>100t |
>100t |
>100t |
>100t |
>100t |
|
50 |
2.692 |
7.107 |
11.47 |
18.42 |
46.90 |
74.36 |
117.4 |
289.0 |
700.2 |
1084. |
1671. |
3927. |
9100. |
70065 |
>100t |
>100t |
>100t |
>100t |
>100t |
>100t indicates that the number exceeds 100 000.
Table 4. Future value of annuity.
The future value of I invested annually at a given rate of interest 'i' for a given number of years 'n'.
Future value of an annuity factor: S (1 + i)n
|
% |
2 |
4 |
5 |
6 |
8 |
9 |
10 |
12 |
14 |
15 |
16 |
18 |
120 |
25 |
30 |
35 |
40 |
50 |
|
Yrs |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
1.02 |
1.04 |
1.05 |
1.06 |
1.08 |
1.09 |
1.1 |
1.12 |
1.14 |
1.15 |
1.16 |
1.18 |
1.2 |
1.25 |
1.3 |
1.35 |
1.4 |
1.5 |
|
2 |
2.060 |
2.122 |
2.153 |
2.184 |
2.246 |
2.278 |
2.310 |
2.374 |
2.440 |
2.473 |
2.506 |
2.572 |
2.640 |
2.813 |
2.990 |
3.173 |
3.360 |
3.750 |
|
3 |
3.122 |
3.246 |
3.310 |
3.375 |
3.506 |
3.573 |
3.641 |
3.779 |
3.921 |
3.993 |
4.066 |
4.215 |
4.368 |
4.766 |
5.187 |
5.633 |
6.104 |
7.125 |
|
4 |
4.204 |
4.416 |
4.526 |
4.637 |
4.867 |
4.985 |
5.105 |
5.353 |
5.610 |
5.742 |
5.877 |
6.154 |
6.442 |
7.207 |
8.043 |
8.954 |
9.946 |
12.19 |
|
5 |
5.308 |
5.633 |
5.802 |
5.975 |
6.336 |
6.523 |
6.716 |
7.115 |
7.536 |
7.754 |
7.977 |
8.442 |
8.930 |
10.26 |
11.76 |
13.44 |
15.32 |
19.78 |
|
6 |
6.434 |
6.898 |
7.142 |
7.394 |
7.923 |
8.200 |
8.487 |
9.089 |
9.730 |
10.07 |
10.41 |
11.14 |
11.92 |
14.07 |
16.58 |
19.49 |
22.85 |
31.17 |
|
7 |
7.583 |
8.214 |
8.549 |
8.897 |
9.637 |
10.03 |
10.44 |
11.30 |
12.23 |
12.73 |
13.24 |
14.33 |
15.50 |
18.84 |
22.86 |
27.66 |
33.39 |
48.26 |
|
8 |
8.755 |
9.583 |
10.03 |
10.49 |
11.49 |
12.02 |
12.58 |
13.78 |
15.09 |
15.79 |
16.52 |
18.09 |
19.80 |
24.80 |
31.01 |
38.70 |
48.15 |
73.89 |
|
9 |
9.950 |
11.01 |
11.58 |
12.18 |
13.49 |
14.19 |
14.94 |
16.55 |
18.34 |
19.30 |
20.32 |
22.52 |
24.96 |
32.25 |
41.62 |
53.59 |
68.81 |
112.3 |
|
10 |
11.17 |
12.49 |
13.21 |
13.97 |
15.65 |
16.56 |
17.53 |
19.65 |
22.04 |
23.35 |
24.73 |
27.76 |
31.15 |
41.57 |
55.41 |
73.70 |
97.74 |
170.0 |
|
11 |
12.41 |
14.03 |
14.92 |
15.87 |
17.98 |
19.14 |
20.38 |
23.13 |
26.27 |
28.00 |
29.85 |
33.93 |
38.58 |
53.21 |
73.33 |
100.8 |
138.2 |
256.5 |
|
12 |
13.68 |
15.63 |
16.71 |
17.88 |
20.50 |
21.95 |
23.52 |
27.03 |
31.09 |
33.35 |
35.79 |
41.22 |
47.50 |
67.76 |
96.63 |
137.5 |
194.9 |
386.2 |
|
13 |
14.97 |
17.29 |
18.60 |
20.02 |
23.21 |
25.02 |
26.97 |
31.39 |
36.58 |
39.50 |
42.67 |
49.82 |
58.20 |
85.95 |
126.9 |
187.0 |
274.3 |
580.9 |
|
14 |
16.29 |
19.02 |
20.58 |
22.28 |
26.15 |
28.36 |
30.77 |
36.28 |
42.84 |
46.58 |
50.66 |
59.97 |
71.04 |
108.7 |
166.3 |
253.7 |
385.4 |
872.8 |
|
15 |
17.64 |
20.82 |
22.66 |
24.67 |
29.32 |
32.00 |
34.95 |
41.75 |
49.98 |
54.72 |
59.93 |
71.94 |
86.44 |
137.1 |
217.5 |
343.9 |
541.0 |
1311. |
|
16 |
19.01 |
22.70 |
24.84 |
27.21 |
32.75 |
35.97 |
39.54 |
47.88 |
58.12 |
64.08 |
70.67 |
86.07 |
104.9 |
172.6 |
284.0 |
465.6 |
758.8 |
1968. |
|
17 |
20.41 |
24.65 |
27.13 |
29.91 |
36.45 |
40.30 |
44.60 |
54.75 |
67.39 |
74.84 |
83.14 |
102.7 |
127.1 |
217.0 |
370.5 |
629.9 |
1064. |
2953. |
|
18 |
21.84 |
26.67 |
29.54 |
32.76 |
40.45 |
45.02 |
50.16 |
62.44 |
77.97 |
87.21 |
97.60 |
122.4 |
153.7 |
272.6 |
483.0 |
851.7 |
1491. |
4431. |
|
19 |
23.30 |
28.78 |
32.07 |
35.79 |
44.76 |
50.16 |
56.27 |
71.05 |
90.02 |
101.4 |
114.4 |
145.6 |
195.7 |
341.9 |
629.2 |
1151. |
2088. |
6648. |
|
20 |
24.78 |
30.97 |
34.72 |
38.99 |
49.42 |
55.76 |
63.00 |
80.70 |
103.8 |
117.8 |
133.8 |
173.0 |
224.0 |
428.7 |
819.2 |
1555. |
2925. |
9973. |
|
21 |
26.30 |
33.25 |
37.51 |
42.39 |
54.46 |
61.87 |
70.40 |
91.50 |
119.4 |
136.6 |
156.4 |
205.3 |
270.0 |
537.1 |
1066. |
2101. |
4096. |
14961 |
|
22 |
27.84 |
35.62 |
40.43 |
46.00 |
59.89 |
68.53 |
78.54 |
103.6 |
137.3 |
158.3 |
182.6 |
243.5 |
325.2 |
672.6 |
1387. |
2838. |
5736. |
22442 |
|
23 |
29.42 |
38.08 |
43.50 |
49.82 |
65.76 |
75.79 |
87.50 |
117.2 |
157.7 |
183.2 |
213.0 |
288.5 |
391.5 |
842.0 |
1805. |
3833. |
8032. |
33665 |
|
24 |
31.03 |
40.65 |
46.73 |
53.86 |
72.11 |
83.70 |
97.35 |
132.3 |
180.9 |
211.8 |
248.2 |
341.6 |
471.0 |
1054. |
2348. |
5176. |
11246 |
50499 |
|
25 |
32.67 |
43.31 |
50.11 |
58.16 |
78.95 |
92.32 |
108.2 |
149.3 |
207.3 |
244.7 |
289.1 |
404.3 |
566.4 |
1318. |
3053. |
6988. |
15746 |
75751 |
|
30 |
41.38 |
58.33 |
69.76 |
83.80 |
122.3 |
148.6 |
180.9 |
270.3 |
406.7 |
500.0 |
615.2 |
933.3 |
1418. |
4034. |
11349 |
31349 |
84702 |
>100t |
|
35 |
50.99 |
76.60 |
94.84 |
118.1 |
186.1 |
235.1 |
298.1 |
483.5 |
790.7 |
1013. |
1300. |
2144. |
3538. |
12321 |
42150 |
>100t |
>100t |
>100t |
|
40 |
61.61 |
98.83 |
126.8 |
164.0 |
279.8 |
368.3 |
486.9 |
859.1 |
1530. |
2046. |
2738. |
4913. |
8813. |
37611 |
>100t |
>100t |
>100t |
>100t |
|
45 |
73.33 |
125.9 |
167.7 |
223.5 |
417.4 |
573.2 |
790.8 |
1521. |
2953. |
4123. |
5760. |
11247 |
21938 |
>100t |
>100t |
>100t |
>100t |
>100t |
|
50 |
86.27 |
158.8 |
219.8 |
307.8 |
619.7 |
888.4 |
1280. |
2688. |
5694. |
8300. |
12105 |
25739 |
54597 |
>100t |
>100t |
>100t |
>100t |
>100t |
> 100t indicates that the number exceeds 100 000. !
Table 5. Annual repayments or capital recovery factors.
The amount that must be repaid annually for every I unit borrowed for 'n' years at 'i' rate of interest.
Capital recovery factor: 1/ [S (1 + i)n]
|
% |
2 |
4 |
5 |
6 |
8 |
9 |
10 |
12 |
14 |
15 |
16 |
18 |
20 |
25 |
30 |
35 |
40 |
45 |
50 |
|
Yrs |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
1.02 |
1.04 |
1.05 |
1.06 |
1.08 |
1.09 |
1.10 |
1.12 |
1.14 |
1.15 |
1.16 |
1.18 |
1.20 |
1.25 |
1.30 |
1.35 |
1.40 |
1.45 |
1.50 |
|
2 |
.515 |
.530 |
.538 |
.545 |
.561 |
.568 |
.576 |
.592 |
.607 |
.615 |
.623 |
.639 |
.655 |
.694 |
.735 |
.776 |
.817 |
.858 |
.900 |
|
3 |
.347 |
.360 |
.367 |
.374 |
.388 |
.395 |
.402 |
.416 |
.431 |
.438 |
.445 |
.460 |
.475 |
.512 |
.551 |
.590 |
.629 |
.670 |
.711 |
|
4 |
.263 |
.275 |
.282 |
.289 |
.302 |
.309 |
.315 |
.329 |
.343 |
.350 |
.357 |
.372 |
.386 |
.423 |
.462 |
.501 |
.541 |
.582 |
.623 |
|
5 |
.212 |
.225 |
.231 |
.237 |
.250 |
.257 |
.264 |
.277 |
.291 |
.298 |
.305 |
.320 |
.334 |
.372 |
.411 |
.450 |
.491 |
.533 |
.576 |
|
6 |
.179 |
.191 |
.197 |
.203 |
.216 |
.223 |
.230 |
.243 |
.257 |
.264 |
.271 |
.286 |
.301 |
.339 |
.378 |
.419 |
.461 |
.504 |
.548 |
|
7 |
.155 |
.167 |
.173 |
.179 |
.192 |
.199 |
.205 |
.219 |
.233 |
.240 |
.248 |
.262 |
.277 |
.316 |
.357 |
.399 |
.442 |
.486 |
.531 |
|
8 |
.137 |
.149 |
.155 |
.161 |
.174 |
.181 |
.187 |
.201 |
.216 |
.223 |
.230 |
.245 |
.261 |
.300 |
.342 |
.385 |
.429 |
.474 |
.520 |
|
9 |
.123 |
.134 |
.141 |
.147 |
.160 |
.167 |
.174 |
.188 |
.202 |
.210 |
.217 |
.232 |
.248 |
.289 |
.331 |
.375 |
.420 |
.466 |
.513 |
|
10 |
.111 |
.123 |
.130 |
.136 |
.149 |
.156 |
.163 |
.177 |
.192 |
.199 |
.207 |
.223 |
.239 |
.280 |
.323 |
.368 |
.414 |
.461 |
.509 |
|
11 |
.102 |
.114 |
.120 |
.127 |
.140 |
.147 |
.154 |
.168 |
.183 |
.191 |
.199 |
.215 |
.231 |
.273 |
.318 |
.363 |
.410 |
.458 |
.506 |
|
12 |
.095 |
.107 |
.113 |
.119 |
.133 |
.140 |
.147 |
.161 |
.177 |
.184 |
.192 |
.209 |
.225 |
.268 |
.313 |
.360 |
.407 |
.455 |
.504 |
|
13 |
.088 |
.100 |
.106 |
.113 |
.127 |
.134 |
.141 |
.156 |
.171 |
.179 |
.187 |
.204 |
.221 |
.265 |
.310 |
.357 |
.405 |
.454 |
.503 |
|
14 |
.083 |
.095 |
.101 |
.108 |
.121 |
.128 |
.136 |
.151 |
.167 |
.175 |
.183 |
.200 |
.217 |
.262 |
.308 |
.355 |
.404 |
.452 |
.502 |
|
15 |
.078 |
.090 |
.096 |
.103 |
.117 |
.124 |
.131 |
.147 |
.163 |
.171 |
.179 |
.196 |
.214 |
.259 |
.306 |
.354 |
.403 |
.452 |
.501 |
|
16 |
.074 |
.086 |
.092 |
.099 |
.113 |
.120 |
.128 |
.143 |
.160 |
.168 |
.176 |
.194 |
.211 |
.257 |
.305 |
.353 |
.402 |
.451 |
.501 |
|
17 |
.070 |
.082 |
.089 |
.095 |
.110 |
.117 |
.125 |
.140 |
.157 |
.165 |
.174 |
.191 |
.209 |
.256 |
.304 |
.352 |
.401 |
.451 |
.501 |
|
18 |
.067 |
.079 |
.086 |
.092 |
.107 |
.114 |
.122 |
.138 |
.155 |
.163 |
.172 |
.190 |
.208 |
.255 |
.303 |
.352 |
.401 |
.451 |
.500 |
|
19 |
.064 |
.076 |
.083 |
.090 |
.104 |
.112 |
.120 |
.136 |
.153 |
.161 |
.170 |
.188 |
.206 |
.254 |
.302 |
.351 |
.401 |
.450 |
.500 |
|
20 |
.061 |
.074 |
.080 |
.087 |
.102 |
.110 |
.117 |
.134 |
.151 |
.160 |
.169 |
.187 |
.205 |
.253 |
.302 |
.351 |
.400 |
.450 |
.500 |
|
21 |
.059 |
.071 |
.078 |
.085 |
.100 |
.109 |
.116 |
.132 |
.150 |
.158 |
.167 |
.186 |
.204 |
.252 |
.301 |
.351 |
.400 |
.450 |
.500 |
|
22 |
.057 |
.069 |
.076 |
.083 |
.098 |
.106 |
.114 |
.131 |
.148 |
.157 |
.166 |
.185 |
.204 |
.252 |
.301 |
.350 |
.400 |
.450 |
.500 |
|
23 |
.055 |
.067 |
.074 |
.081 |
.096 |
.104 |
.113 |
.130 |
.147 |
.156 |
.165 |
.184 |
.203 |
.251 |
.301 |
.350 |
.400 |
.450 |
.500 |
|
24 |
.053 |
.066 |
.072 |
.080 |
.095 |
.103 |
.111 |
.128 |
.146 |
.155 |
.165 |
.183 |
.203 |
.251 |
.301 |
.350 |
.400 |
.450 |
.500 |
|
25 |
.051 |
.064 |
.071 |
.078 |
.094 |
.102 |
.110 |
.127 |
.145 |
.155 |
.164 |
.183 |
.202 |
.251 |
.300 |
.350 |
.400 |
.450 |
.500 |
|
30 |
.045 |
.058 |
.065 |
.073 |
.089 |
.097 |
.106 |
.124 |
.143 |
.152 |
.162 |
.181 |
.201 |
.250 |
.300 |
.350 |
A00 |
.450 |
.500 |
|
35 |
.040 |
.054 |
.061 |
.069 |
.086 |
.095 |
.104 |
.122 |
.141 |
.151 |
.161 |
.181 |
.200 |
.250 |
.300 |
.350 |
.400 |
.450 |
.500 |
|
40 |
.037 |
.051 |
.058 |
.066 |
.084 |
.093 |
.102 |
.121 |
.141 |
.151 |
.161 |
.181 |
.200 |
.250 |
.300 |
.350 |
.400 |
.450 |
.500 |
|
45 |
.034 |
.048 |
.056 |
.065 |
.083 |
.092 |
.101 |
.121 |
.140 |
.150 |
.160 |
.180 |
.200 |
.250 |
.300 |
.350 |
.400 |
.450 |
.500 |
|
50 |
.032 |
.047 |
.055 |
.063 |
.082 |
.091 |
.101 |
.120 |
.140 |
.150 |
.160 |
.180 |
.200 |
.250 |
.300 |
.350 |
.400 |
.450 |
.500 |
Table 6. Random numbers.
|
52687 |
36466 |
31250 |
10750 |
81154 |
76239 |
02937 |
00804 |
14571 |
35636 |
99891 |
39300 |
20363 |
81053 |
|
87126 |
68315 |
66018 |
99258 |
23050 |
51628 |
95686 |
65633 |
03927 |
49542 |
62015 |
76279 |
30667 |
47457 |
|
08370 |
55493 |
80297 |
42941 |
53954 |
89751 |
81720 |
75500 |
52079 |
18983 |
09517 |
54467 |
43840 |
05978 |
|
64461 |
88503 |
13868 |
38579 |
51074 |
06421 |
11489 |
91794 |
58253 |
16172 |
43289 |
36508 |
92507 |
19955 |
|
47069 |
69382 |
72355 |
41264 |
76842 |
44975 |
72445 |
60619 |
76206 |
78458 |
57261 |
20480 |
14159 |
77540 |
|
11049 |
93629 |
75978 |
09284 |
74560 |
35337 |
41350 |
19829 |
72905 |
81083 |
18417 |
09269 |
04931 |
02875 |
|
66460 |
78901 |
90850 |
56802 |
64686 |
00483 |
84721 |
02891 |
04851 |
28690 |
78929 |
55718 |
76640 |
34683 |
|
24470 |
72028 |
81587 |
94552 |
19714 |
14725 |
30418 |
50040 |
10905 |
21456 |
96274 |
21497 |
71360 |
84488 |
|
27826 |
38847 |
42635 |
00011 |
44324 |
87077 |
86266 |
36286 |
52016 |
02138 |
99081 |
33774 |
60456 |
86-051 |
|
92892 |
00108 |
80450 |
08016 |
34409 |
63265 |
03569 |
53389 |
94802 |
78443 |
14874 |
34622 |
01461 |
12809 |
|
75493 |
85249 |
68259 |
78254 |
04969 |
90573 |
80572 |
22936 |
75494 |
65843 |
54777 |
82846 |
07602 |
12542 |
|
13438 |
38729 |
51739 |
21464 |
23261 |
50418 |
88106 |
84632 |
13687 |
13245 |
91385 |
54043 |
49706 |
01643 |
|
92906 |
70078 |
94555 |
90339 |
44937 |
93688 |
03769 |
35063 |
29841 |
00717 |
55934 |
92701 |
55639 |
92813 |
|
52547 |
32590 |
50596 |
85757 |
17311 |
50801 |
05721 |
06699 |
59503 |
06371 |
57022 |
46540 |
51404 |
87963 |
|
87201 |
72295 |
93739 |
92461 |
86958 |
93697 |
84126 |
18507 |
15149 |
68452 |
10995 |
18637 |
63589 |
10291 |
|
34068 |
50072 |
01118 |
19281 |
78744 |
46676 |
26528 |
60506 |
84982 |
55870 |
85367 |
84104 |
62187 |
75449 |
|
71417 |
95366 |
24359 |
76252 |
95341 |
59073 |
91119 |
15355 |
25554 |
72685 |
71664 |
41397 |
85554 |
18196 |
|
80180 |
91959 |
07223 |
59851 |
13118 |
7,8283 |
55640 |
89046 |
36486 |
58435 |
91206 |
29737 |
73846 |
81192 |
|
03205 |
96028 |
75043 |
51927 |
06520 |
35374 |
13506 |
86271 |
17397 |
38235 |
89714 |
63479 |
99097 |
57960 |
|
64607 |
89019 |
08505 |
68026 |
46860 |
04838 |
47212 |
07890 |
53116 |
61106 |
64073 |
75536 |
37865 |
65796 |
