【例题8·计算分析题】20×0年1月1日，XYZ公司支付价款1 000元（含交易费用），从活跃市场上购入某公司5年期债券，面值1 250元，票面年利率4.72%，按年支付利息（即每年支付59元），本金最后一次支付。合同约定，该债券的发行方在遇到特定情况时可以将债券赎回，且不需要为提前赎回支付额外款项。XYZ公司在购买该债券时，预计发行方不会提前赎回。
XYZ公司将购入的该公司债券划分为持有至到期投资，且不考虑所得税、减值损失等因素。为此，XYZ公司在初始确认时先计算确定该债券的实际利率：
第一种：
设该债券的实际利率为r，则可列出如下等式：
59×（1+r）-1+59×（1+r）-2+59×（1+r）-3+59×（1+r）-4+（59+1 250）×（1+r）-5=1 000（元）
第二种：
59×（P/A，i，5）+1250×（P/F，i，5）=1000（元）
试算法:
查表：
59×（1+5%）-1+59×（1+5%）-2+59×（1+5%）-3+59×（1+5%）-4+（59+1 250）×（1+5%）-5= 1 234.04 （元）
59×（1+6%）-1+59×（1+6%）-2+59×（1+6%）-3+59×（1+6%）-4+（59+1 250）×（1+6%）-5=1 182.60 （元）
59×（1+7%）-1+59×（1+7%）-2+59×（1+7%）-3+59×（1+7%）-4+（59+1 250）×（1+7%）-5= 1 133.14（元）
8%——9% 的计算省略。
59×（1+10%）-1+59×（1+10%）-2+59×（1+10%）-3+59×（1+10%）-4+（59+1 250）×（1+10%）-5=1 000（元）
把10%的复利现值系数代入：59×0.909 + 59×0.826 + 59×0.751 + 59×0.683 +（59+1 250）×0.62=53.631+48.734+44.309+40.297+811.58≈1 000（元）
复利现值系数表
| 5% |
6% |
8% |
10% |
|
0.952 |
0.943 |
0.925 |
0.909 |
|
0.907 |
0.889 |
0.857 |
0.826 |
|
0.863 |
0.839 |
0.793 |
0.751 |
|
0.822 |
0.792 |
0.735 |
0.683 |
|
0.783 |
0.747 |
0.68 |
0.62 |
（P/F 5% 5）=0.784
| 复利现值系数表（P/F表） |
|
n |
1% |
2% |
3% |
4% |
5% |
6% |
8% |
10% |
12% |
14% |
15% |
16% |
18% |
|
1 |
0.99 |
0.98 |
0.97 |
0.961 |
0.952 |
0.943 |
0.925 |
0.909 |
0.892 |
0.877 |
0.869 |
0.862 |
0.847 |
|
2 |
0.98 |
0.961 |
0.942 |
0.924 |
0.907 |
0.889 |
0.857 |
0.826 |
0.797 |
0.769 |
0.756 |
0.743 |
0.718 |
|
3 |
0.97 |
0.942 |
0.915 |
0.888 |
0.863 |
0.839 |
0.793 |
0.751 |
0.711 |
0.674 |
0.657 |
0.64 |
0.608 |
|
4 |
0.96 |
0.923 |
0.888 |
0.854 |
0.822 |
0.792 |
0.735 |
0.683 |
0.635 |
0.592 |
0.571 |
0.552 |
0.515 |
|
5 |
0.951 |
0.905 |
0.862 |
0.821 |
0.784 |
0.747 |
0.68 |
0.62 |
0.567 |
0.519 |
0.497 |
0.476 |
0.437 |
|
6 |
0.942 |
0.887 |
0.837 |
0.79 |
0.746 |
0.704 |
0.63 |
0.564 |
0.506 |
0.455 |
0.432 |
0.41 |
0.37 |
|
7 |
0.932 |
0.87 |
0.813 |
0.759 |
0.71 |
0.665 |
0.583 |
0.513 |
0.452 |
0.399 |
0.375 |
0.353 |
0.313 |
|
8 |
0.923 |
0.853 |
0.789 |
0.73 |
0.676 |
0.627 |
0.54 |
0.466 |
0.403 |
0.35 |
0.326 |
0.305 |
0.266 |
|
9 |
0.914 |
0.836 |
0.766 |
0.702 |
0.644 |
0.591 |
0.5 |
0.424 |
0.36 |
0.307 |
0.284 |
0.262 |
0.225 |
|
10 |
0.905 |
0.82 |
0.744 |
0.675 |
0.613 |
0.558 |
0.463 |
0.385 |
0.321 |
0.269 |
0.247 |
0.226 |
0.191 |
|
11 |
0.896 |
0.804 |
0.722 |
0.649 |
0.584 |
0.526 |
0.428 |
0.35 |
0.287 |
0.236 |
0.214 |
0.195 |
0.161 |
|
12 |
0.887 |
0.788 |
0.701 |
0.624 |
0.556 |
0.496 |
0.397 |
0.318 |
0.256 |
0.207 |
0.186 |
0.168 |
0.137 |
|
13 |
0.878 |
0.773 |
0.68 |
0.6 |
0.53 |
0.468 |
0.367 |
0.289 |
0.229 |
0.182 |
0.162 |
0.145 |
0.116 |
|
14 |
0.869 |
0.757 |
0.661 |
0.577 |
0.505 |
0.442 |
0.34 |
0.263 |
0.204 |
0.159 |
0.141 |
0.125 |
0.098 |
|
15 |
0.861 |
0.743 |
0.641 |
0.555 |
0.481 |
0.417 |
0.315 |
0.239 |
0.182 |
0.14 |
0.122 |
0.107 |
0.083 |
|
16 |
0.852 |
0.728 |
0.623 |
0.533 |
0.458 |
0.393 |
0.291 |
0.217 |
0.163 |
0.122 |
0.106 |
0.093 |
0.07 |
|
17 |
0.844 |
0.714 |
0.605 |
0.513 |
0.436 |
0.371 |
0.27 |
0.197 |
0.145 |
0.107 |
0.092 |
0.08 |
0.059 |
|
18 |
0.836 |
0.7 |
0.587 |
0.493 |
0.415 |
0.35 |
0.25 |
0.179 |
0.13 |
0.094 |
0.08 |
0.069 |
0.05 |
|
19 |
0.827 |
0.686 |
0.57 |
0.474 |
0.395 |
0.33 |
0.231 |
0.163 |
0.116 |
0.082 |
0.07 |
0.059 |
0.043 |
|
20 |
0.819 |
0.672 |
0.553 |
0.456 |
0.376 |
0.311 |
0.214 |
0.148 |
0.103 |
0.072 |
0.061 |
0.051 |
0.036 |
(F/P 5% 5)=1.276
|
复利终值系数表（F/P表） |
|
|
1% |
2% |
3% |
4% |
5% |
6% |
7% |
8% |
9% |
10% |
11% |
|
1 |
1.010 |
1.020 |
1.030 |
1.040 |
1.050 |
1.060 |
1.070 |
1.080 |
1.090 |
1.100 |
1.110 |
|
2 |
1.020 |
1.040 |
1.061 |
1.082 |
1.103 |
1.124 |
1.145 |
1.166 |
1.188 |
1.210 |
1.232 |
|
3 |
1.030 |
1.061 |
1.093 |
1.125 |
1.158 |
1.191 |
1.225 |
1.260 |
1.295 |
1.331 |
1.368 |
|
4 |
1.041 |
1.082 |
1.126 |
1.170 |
1.216 |
1.262 |
1.311 |
1.360 |
1.412 |
1.464 |
1.518 |
|
5 |
1.051 |
1.104 |
1.159 |
1.217 |
1.276 |
1.338 |
1.403 |
1.469 |
1.539 |
1.611 |
1.685 |
|
6 |
1.062 |
1.126 |
1.194 |
1.265 |
1.340 |
1.419 |
1.501 |
1.587 |
1.677 |
1.772 |
1.870 |
|
7 |
1.072 |
1.149 |
1.230 |
1.316 |
1.407 |
1.504 |
1.606 |
1.714 |
1.828 |
1.949 |
2.076 |
|
8 |
1.083 |
1.172 |
1.267 |
1.369 |
1.477 |
1.594 |
1.718 |
1.851 |
1.993 |
2.144 |
2.305 |
|
9 |
1.094 |
1.195 |
1.305 |
1.423 |
1.551 |
1.689 |
1.838 |
1.999 |
2.172 |
2.358 |
2.558 |
|
10 |
1.105 |
1.219 |
1.344 |
1.480 |
1.629 |
1.791 |
1.967 |
2.159 |
2.367 |
2.594 |
2.839 |
|
11 |
1.116 |
1.243 |
1.384 |
1.539 |
1.710 |
1.898 |
2.105 |
2.332 |
2.580 |
2.853 |
3.152 |
|
12 |
1.127 |
1.268 |
1.426 |
1.601 |
1.796 |
2.012 |
2.252 |
2.518 |
2.813 |
3.138 |
3.498 |
|
13 |
1.138 |
1.294 |
1.469 |
1.665 |
1.886 |
2.133 |
2.410 |
2.720 |
3.066 |
3.452 |
3.883 |
|
14 |
1.149 |
1.319 |
1.513 |
1.732 |
1.980 |
2.261 |
2.579 |
2.937 |
3.342 |
3.797 |
4.310 |
|
15 |
1.161 |
1.346 |
1.558 |
1.801 |
2.079 |
2.397 |
2.759 |
3.172 |
3.642 |
4.177 |
4.785 |
|
16 |
1.173 |
1.373 |
1.605 |
1.873 |
2.183 |
2.540 |
2.952 |
3.426 |
3.970 |
4.595 |
5.311 |
|
17 |
1.184 |
1.400 |
1.653 |
1.948 |
2.292 |
2.693 |
3.159 |
3.700 |
4.328 |
5.054 |
5.895 |
|
18 |
1.196 |
1.428 |
1.702 |
2.026 |
2.407 |
2.854 |
3.380 |
3.996 |
4.717 |
5.560 |
6.544 |
|
19 |
1.208 |
1.457 |
1.754 |
2.107 |
2.527 |
3.026 |
3.617 |
4.316 |
5.142 |
6.116 |
7.263 |
|
20 |
1.220 |
1.486 |
1.806 |
2.191 |
2.653 |
3.207 |
3.870 |
4.661 |
5.604 |
6.727 |
8.062 |
|
21 |
1.232 |
1.516 |
1.860 |
2.279 |
2.786 |
3.400 |
4.141 |
5.034 |
6.109 |
7.400 |
8.949 |
|
22 |
1.245 |
1.546 |
1.916 |
2.370 |
2.925 |
3.604 |
4.430 |
5.437 |
6.659 |
8.140 |
9.934 |
|
23 |
1.257 |
1.577 |
1.974 |
2.465 |
3.072 |
3.820 |
4.741 |
5.871 |
7.258 |
8.954 |
11.026 |
|
24 |
1.270 |
1.608 |
2.033 |
2.563 |
3.225 |
4.049 |
5.072 |
6.341 |
7.911 |
9.850 |
12.239 |
|
25 |
1.282 |
1.641 |
2.094 |
2.666 |
3.386 |
4.292 |
5.427 |
6.848 |
8.623 |
10.835 |
13.585 |
|
年金现值系数表（P/A表） |
|
n |
1% |
2% |
3% |
4% |
5% |
6% |
8% |
10% |
12% |
|
1 |
0.99 |
0.98 |
0.97 |
0.961 |
0.952 |
0.943 |
0.925 |
0.909 |
0.892 |
|
2 |
1.97 |
1.941 |
1.913 |
1.886 |
1.859 |
1.833 |
1.783 |
1.735 |
1.69 |
|
3 |
2.94 |
2.883 |
2.828 |
2.775 |
2.723 |
2.673 |
2.577 |
2.486 |
2.401 |
|
4 |
3.901 |
3.807 |
3.717 |
3.629 |
3.545 |
3.465 |
3.312 |
3.169 |
3.037 |
|
5 |
4.853 |
4.713 |
4.579 |
4.451 |
4.329 |
4.212 |
3.992 |
3.79 |
3.604 |
|
6 |
5.795 |
5.601 |
5.417 |
5.242 |
5.075 |
4.917 |
4.622 |
4.355 |
4.111 |
|
7 |
6.728 |
6.471 |
6.23 |
6.002 |
5.786 |
5.582 |
5.206 |
4.868 |
4.563 |
|
8 |
7.651 |
7.325 |
7.019 |
6.732 |
6.463 |
6.209 |
5.746 |
5.334 |
4.967 |
|
9 |
8.566 |
8.162 |
7.786 |
7.435 |
7.107 |
6.801 |
6.246 |
5.759 |
5.328 |
|
10 |
9.471 |
8.982 |
8.53 |
8.11 |
7.721 |
7.36 |
6.71 |
6.1446 |
5.65 |
|
11 |
10.367 |
9.786 |
9.252 |
8.76 |
8.306 |
7.886 |
7.138 |
6.495 |
5.937 |
|
12 |
11.255 |
10.575 |
9.954 |
9.385 |
8.863 |
8.383 |
7.536 |
6.813 |
6.194 |
|
13 |
12.133 |
11.348 |
10.634 |
9.985 |
9.393 |
8.852 |
7.903 |
7.103 |
6.423 |
|
14 |
13.003 |
12.106 |
11.296 |
10.563 |
9.898 |
9.294 |
8.244 |
7.366 |
6.628 |
|
15 |
13.865 |
12.849 |
11.937 |
11.118 |
10.379 |
9.712 |
8.559 |
7.606 |
6.81 |
|
16 |
14.717 |
13.577 |
12.561 |
11.652 |
10.837 |
10.105 |
8.851 |
7.823 |
6.973 |
|
17 |
15.562 |
14.291 |
13.166 |
12.165 |
11.274 |
10.477 |
9.121 |
8.021 |
7.119 |
|
18 |
16.398 |
14.992 |
13.753 |
12.659 |
11.689 |
10.827 |
9.371 |
8.201 |
7.249 |
|
19 |
17.226 |
15.678 |
14.323 |
13.133 |
12.085 |
11.158 |
9.603 |
8.364 |
7.365 |
|
20 |
18.045 |
16.351 |
14.877 |
13.59 |
12.462 |
11.469 |
9.818 |
8.513 |
7.469 |
|
21 |
18.856 |
17.011 |
15.415 |
14.029 |
12.821 |
11.764 |
10.016 |
8.648 |
7.562 |
|
22 |
19.66 |
17.658 |
15.936 |
14.451 |
13.163 |
12.041 |
10.2 |
8.771 |
7.644 |
|
23 |
20.455 |
18.292 |
16.443 |
14.856 |
13.488 |
12.303 |
10.371 |
8.883 |
7.718 |
|
24 |
21.243 |
18.913 |
16.935 |
15.246 |
13.798 |
12.55 |
10.528 |
8.984 |
7.784 |
|
年金终值系数表（F/A表） |
|
n |
1% |
2% |
3% |
4% |
5% |
6% |
7% |
8% |
9% |
10% |
|
1 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
|
2 |
2.010 |
2.020 |
2.030 |
2.040 |
2.050 |
2.060 |
2.070 |
2.080 |
2.090 |
2.100 |
|
3 |
3.030 |
3.060 |
3.091 |
3.122 |
3.153 |
3.184 |
3.215 |
3.246 |
3.278 |
3.310 |
|
4 |
4.060 |
4.122 |
4.184 |
4.246 |
4.310 |
4.375 |
4.440 |
4.506 |
4.573 |
4.641 |
|
5 |
5.101 |
5.204 |
5.309 |
5.416 |
5.526 |
5.637 |
5.751 |
5.867 |
5.985 |
6.105 |
|
6 |
6.152 |
6.308 |
6.468 |
6.633 |
6.802 |
6.975 |
7.153 |
7.336 |
7.523 |
7.716 |
|
7 |
7.214 |
7.434 |
7.662 |
7.898 |
8.142 |
8.394 |
8.654 |
8.923 |
9.200 |
9.487 |
|
8 |
8.286 |
8.583 |
8.892 |
9.214 |
9.549 |
9.879 |
10.260 |
10.637 |
11.028 |
11.436 |
|
9 |
9.369 |
9.755 |
10.159 |
10.583 |
11.027 |
11.491 |
11.978 |
12.488 |
13.021 |
13.579 |
|
10 |
10.462 |
10.950 |
11.464 |
12.006 |
12.578 |
13.181 |
13.816 |
14.487 |
15.913 |
15.937 |
|
11 |
11.567 |
12.169 |
12.808 |
13.486 |
14.207 |
14.972 |
15.784 |
16.645 |
17.560 |
18.531 |
|
12 |
12.683 |
13.412 |
14.192 |
15.026 |
16.917 |
16.870 |
17.888 |
18.977 |
20.141 |
21.384 |
|
13 |
13.809 |
14.680 |
15.618 |
16.627 |
17.713 |
18.882 |
20.141 |
21.495 |
22.953 |
24.523 |
|
14 |
14.947 |
15.974 |
17.086 |
18.292 |
19.599 |
21.015 |
22.550 |
24.215 |
26.019 |
27.975 |
|
15 |
16.097 |
17.293 |
18.599 |
20.024 |
21.579 |
23.276 |
25.129 |
27.152 |
29.361 |
31.772 |
|
16 |
17.258 |
18.639 |
20.157 |
21.825 |
23.657 |
25.673 |
27.888 |
30.324 |
33.003 |
35.950 |
|
17 |
18.430 |
20.012 |
21.762 |
23.698 |
25.840 |
28.213 |
30.840 |
33.750 |
36.974 |
40.545 |
|
18 |
19.615 |
21.412 |
23.414 |
25.645 |
28.132 |
30.906 |
33.999 |
37.450 |
41.301 |
45.599 |
|
19 |
20.811 |
22.841 |
25.117 |
27.671 |
30.539 |
33.760 |
37.379 |
41.446 |
46.018 |
51.159 |
|
20 |
22.019 |
24.297 |
26.870 |
29.778 |
33.066 |
36.786 |
40.995 |
45.762 |
51.160 |
57.275 |
