一定期间内每期期末等额的系列收付款项的现值之和,叫后付年金现值。后付年金现值的符号为PVAn,后付年金现值的计算公式为:
式中,
有关年金现值系数值,可通过年金现值系数表查得。
例如,现在存入一笔钱,准备在以后5年中每年末得到100元,如果利息率为10%,现在应存入多少钱?在本例中,通过“年金现值系数”查表可得,PVIFA10%,5 = 3.790,则:
=379
附:年金现值系数表
n | 1% | 2% | 3% | 4% | 5% | 6% | 8% | 10% | 12% | 14% | 15% | 16% | 18% | 20% | 22% | 24% | 25% | 30% | 35% | 40% | 45% | 50% |
1 | 0.990 | 0.980 | 0.970 | 0.961 | 0.952 | 0.943 | 0.925 | 0.909 | 0.892 | 0.877 | 0.869 | 0.862 | 0.847 | 0.833 | 0.819 | 0.806 | 0.799 | 0.769 | 0.740 | 0.714 | 0.689 | 0.666 |
2 | 1.970 | 1.941 | 1.913 | 1.886 | 1.859 | 1.833 | 1.783 | 1.735 | 1.690 | 1.646 | 1.625 | 1.605 | 1.565 | 1.527 | 1.491 | 1.456 | 1.44 | 1.360 | 1.289 | 1.224 | 1.165 | 1.111 |
3 | 2.940 | 2.883 | 2.828 | 2.775 | 2.723 | 2.673 | 2.577 | 2.486 | 2.401 | 2.321 | 2.283 | 2.245 | 2.174 | 2.106 | 2.042 | 1.981 | 1.952 | 1.816 | 1.695 | 1.588 | 1.493 | 1.407 |
4 | 3.901 | 3.807 | 3.717 | 3.629 | 3.545 | 3.465 | 3.312 | 3.169 | 3.037 | 2.913 | 2.854 | 2.798 | 2.690 | 2.588 | 2.493 | 2.404 | 2.361 | 2.166 | 1.996 | 1.849 | 1.719 | 1.604 |
5 | 4.853 | 4.713 | 4.579 | 4.451 | 4.329 | 4.212 | 3.992 | 3.790 | 3.604 | 3.433 | 3.352 | 3.274 | 3.127 | 2.990 | 2.863 | 2.745 | 2.689 | 2.435 | 2.219 | 2.035 | 1.875 | 1.736 |
6 | 5.795 | 5.601 | 5.417 | 5.242 | 5.075 | 4.917 | 4.622 | 4.355 | 4.111 | 3.888 | 3.784 | 3.684 | 3.497 | 3.325 | 3.166 | 3.020 | 2.951 | 2.642 | 2.385 | 2.167 | 1.983 | 1.824 |
7 | 6.728 | 6.471 | 6.230 | 6.002 | 5.786 | 5.582 | 5.206 | 4.868 | 4.563 | 4.288 | 4.160 | 4.038 | 3.811 | 3.604 | 3.415 | 3.242 | 3.161 | 2.802 | 2.507 | 2.262 | 2.057 | 1.882 |
8 | 7.651 | 7.325 | 7.019 | 6.732 | 6.463 | 6.209 | 5.746 | 5.334 | 4.967 | 4.638 | 4.487 | 4.343 | 4.077 | 3.837 | 3.619 | 3.421 | 3.328 | 2.924 | 2.598 | 2.330 | 2.108 | 1.921 |
9 | 8.566 | 8.162 | 7.786 | 7.435 | 7.107 | 6.801 | 6.246 | 5.759 | 5.328 | 4.946 | 4.771 | 4.606 | 4.303 | 4.030 | 3.786 | 3.565 | 3.463 | 3.019 | 2.665 | 2.378 | 2.143 | 1.947 |
10 | 9.471 | 8.982 | 8.530 | 8.110 | 7.721 | 7.360 | 6.710 | 6.144 | 5.650 | 5.216 | 5.018 | 4.833 | 4.494 | 4.192 | 3.923 | 3.681 | 3.570 | 3.091 | 2.715 | 2.413 | 2.168 | 1.965 |
11 | 10.367 | 9.786 | 9.252 | 8.760 | 8.306 | 7.886 | 7.138 | 6.495 | 5.937 | 5.452 | 5.233 | 5.028 | 4.656 | 4.327 | 4.035 | 3.775 | 3.656 | 3.147 | 2.751 | 2.438 | 2.184 | 1.976 |
12 | 11.255 | 10.575 | 9.954 | 9.385 | 8.863 | 8.383 | 7.536 | 6.813 | 6.194 | 5.660 | 5.420 | 5.197 | 4.793 | 4.439 | 4.127 | 3.851 | 3.725 | 3.190 | 2.779 | 2.455 | 2.196 | 1.984 |
13 | 12.133 | 11.348 | 10.634 | 9.985 | 9.393 | 8.852 | 7.903 | 7.103 | 6.423 | 5.842 | 5.583 | 5.342 | 4.909 | 4.532 | 4.202 | 3.912 | 3.780 | 3.223 | 2.799 | 2.468 | 2.204 | 1.989 |
14 | 13.003 | 12.106 | 11.296 | 10.563 | 9.898 | 9.294 | 8.244 | 7.366 | 6.628 | 6.002 | 5.724 | 5.467 | 5.008 | 4.610 | 4.264 | 3.961 | 3.824 | 3.248 | 2.814 | 2.477 | 2.209 | 1.993 |
15 | 13.865 | 12.849 | 11.937 | 11.118 | 10.379 | 9.712 | 8.559 | 7.606 | 6.810 | 6.142 | 5.847 | 5.575 | 5.091 | 4.675 | 4.315 | 4.001 | 3.859 | 3.268 | 2.825 | 2.483 | 2.213 | 1.995 |
16 | 14.717 | 13.577 | 12.561 | 11.652 | 10.837 | 10.105 | 8.851 | 7.823 | 6.973 | 6.265 | 5.954 | 5.668 | 5.162 | 4.729 | 4.356 | 4.033 | 3.887 | 3.283 | 2.833 | 2.488 | 2.216 | 1.996 |
17 | 15.562 | 14.291 | 13.166 | 12.165 | 11.274 | 10.477 | 9.121 | 8.021 | 7.119 | 6.372 | 6.047 | 5.748 | 5.222 | 4.774 | 4.390 | 4.059 | 3.909 | 3.294 | 2.839 | 2.491 | 2.218 | 1.997 |
18 | 16.398 | 14.992 | 13.753 | 12.659 | 11.689 | 10.827 | 9.371 | 8.201 | 7.249 | 6.467 | 6.127 | 5.817 | 5.273 | 4.812 | 4.418 | 4.079 | 3.927 | 3.303 | 2.844 | 2.494 | 2.219 | 1.998 |
19 | 17.226 | 15.678 | 14.323 | 13.133 | 12.085 | 11.158 | 9.603 | 8.364 | 7.365 | 6.550 | 6.198 | 5.877 | 5.316 | 4.843 | 4.441 | 4.096 | 3.942 | 3.310 | 2.847 | 2.495 | 2.220 | 1.999 |
20 | 18.045 | 16.351 | 14.877 | 13.590 | 12.462 | 11.469 | 9.818 | 8.513 | 7.469 | 6.623 | 6.259 | 5.928 | 5.352 | 4.869 | 4.460 | 4.110 | 3.953 | 3.315 | 2.850 | 2.497 | 2.220 | 1.999 |
21 | 18.856 | 17.011 | 15.415 | 14.029 | 12.821 | 11.764 | 10.016 | 8.648 | 7.562 | 6.686 | 6.312 | 5.973 | 5.383 | 4.891 | 4.475 | 4.121 | 3.963 | 3.319 | 2.851 | 2.497 | 2.221 | 1.999 |
22 | 19.660 | 17.658 | 15.936 | 14.451 | 13.163 | 12.041 | 10.200 | 8.771 | 7.644 | 6.742 | 6.358 | 6.011 | 5.409 | 4.909 | 4.488 | 4.129 | 3.970 | 3.322 | 2.853 | 2.498 | 2.221 | 1.999 |
23 | 20.455 | 18.292 | 16.443 | 14.856 | 13.488 | 12.303 | 10.371 | 8.883 | 7.718 | 6.792 | 6.398 | 6.044 | 5.432 | 4.924 | 4.498 | 4.137 | 3.976 | 3.325 | 2.854 | 2.498 | 2.221 | 1.999 |
24 | 21.243 | 18.913 | 16.935 | 15.246 | 13.798 | 12.550 | 10.528 | 8.984 | 7.784 | 6.835 | 6.433 | 6.072 | 5.450 | 4.937 | 4.507 | 4.142 | 3.981 | 3.327 | 2.855 | 2.499 | 2.221 | 1.999 |
25 | 22.023 | 19.523 | 17.413 | 15.622 | 14.093 | 12.783 | 10.674 | 9.077 | 7.843 | 6.872 | 6.464 | 6.097 | 5.466 | 4.947 | 4.513 | 4.147 | 3.984 | 3.328 | 2.855 | 2.499 | 2.222 | 1.999 |
26 | 22.795 | 20.121 | 17.876 | 15.982 | 14.375 | 13.003 | 10.809 | 9.160 | 7.895 | 6.906 | 6.490 | 6.118 | 5.480 | 4.956 | 4.519 | 4.151 | 3.987 | 3.329 | 2.855 | 2.499 | 2.222 | 1.999 |
27 | 23.559 | 20.706 | 18.327 | 16.329 | 14.643 | 13.210 | 10.935 | 9.237 | 7.942 | 6.935 | 6.513 | 6.136 | 5.491 | 4.963 | 4.524 | 4.154 | 3.990 | 3.330 | 2.856 | 2.499 | 2.222 | 1.999 |
28 | 24.316 | 21.281 | 18.764 | 16.663 | 14.898 | 13.406 | 11.051 | 9.306 | 7.984 | 6.960 | 6.533 | 6.152 | 5.501 | 4.969 | 4.528 | 4.156 | 3.992 | 3.331 | 2.856 | 2.499 | 2.222 | 1.999 |
29 | 25.065 | 21.844 | 19.188 | 16.983 | 15.141 | 13.590 | 11.158 | 9.369 | 8.021 | 6.983 | 6.550 | 6.165 | 5.509 | 4.974 | 4.531 | 4.158 | 3.993 | 3.331 | 2.856 | 2.499 | 2.222 | 1.999 |
30 | 25.807 | 22.396 | 19.600 | 17.292 | 15.372 | 13.764 | 11.257 | 9.426 | 8.055 | 7.002 | 6.565 | 6.177 | 5.516 | 4.978 | 4.533 | 4.160 | 3.995 | 3.332 | 2.856 | 2.499 | 2.222 | 1.999 |
40 | 32.834 | 27.355 | 23.114 | 19.792 | 17.159 | 15.046 | 11.924 | 9.779 | 8.243 | 7.105 | 6.641 | 6.233 | 5.548 | 4.996 | 4.543 | 4.165 | 3.999 | 3.333 | 2.857 | 2.499 | 2.222 | 1.999 |
50 | 39.196 | 31.423 | 25.729 | 21.482 | 18.255 | 15.761 | 12.233 | 9.914 | 8.304 | 7.132 | 6.660 | 6.246 | 5.554 | 4.999 | 4.545 | 4.166 | 3.999 | 3.333 | 2.857 | 2.499 | 2.222 | 1.999 |
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