一 : 年金现值表 复利现值系数表

年金现值表

-n

计算公式：P=A*(P/A，i，n)=A*[1-（1＋i） ]/i，其中(P/A，i，n)称作“年金现值系数”

期数 1 2 3 4 5 6 7 8 9

1.0%

2.0%

3.0%

4.0%

14% 0.87721.64672.32162.91373.43313.88874.28834.63894.94645.21615.45275.66035.84246.00216.14226.26516.37296.46746.55046.62316.68706.74296.7921

0.86961.62572.28322.85503.35223.78454.16044.48734.77165.01885.23375.42065.58315.72455.84745.95426.04726.12806.19826.25936.31256.35876.3988

3.2743 3.1993 4.8332 4.6586 5.5755 5.3242 5.9288 5.6278 0.990 0.980 1.970 1.942 2.941 2.884 3.902 3.808 4.583 4.713 5.795 5.601 6.728 6.472 7.652 7.325 8.566 8.162

0.971 0.962 0.88501.913 1.886 1.66812.829 2.775 2.36123.717 3.630 2.97454.580 4.452 4.329 4.212 4.100 3.993 3.890 3.791 3.696 3.605 3.51725.417 5.242 3.99756.230 6.002 4.42267.020 6.733 4.79887.786 7.435 5.13178.530 8.111 7.722 7.360 7.024 6.710 6.418 6.145 5.889 5.650 5.42629.253 8.760 5.68699.954 9.385 5.9176

9.986 6.1218

10 9.471 8.983 9.787 10.575

11.348 10.635

12.106 11.296 6.302515 13.865 12.849 11.938 11.118 10.380 9.712 9.108 8.559 8.061 7.606 7.191 6.811 6.462413.578 12.561 10.10614.292 13.166 10.47714.992 13.754 6.60396.729110.059

6.83996.93809.818 9.129 8.514 7.963 7.469 7.02487.10167.16957.2297

15.678 14.324 20 18.046 16.351 14.877 13.590 12.462 11.470 10.59417.011 15.415 17.658 15.937 18.292 16.444 11.06111.272

复利现值系数表 年金现值表 复利现值系数表

18.914 16.936 25 22.023 19.523 17.413 15.622 14.094 12.78320.121 17.877 21.281 18.764 21.844 19.188 30 25.808 22.396 19.600 17.292 15.372 13.76522.938 20.000 23.468 20.389 23.989 20.766 24.499 21.132 35 29.409 24.999 21.487 18.665 16.374 14.49825.489 21.832 25.969 22.167 26.441 22.492 26.903 22.808 40 32.835 27.355 23.115 19.793 17.159 15.04627.799 23.412 28.235 23.701 28.662 23.982 29.080 24.254 45 36.095 29.490 24.519 20.720 17.774 15.45629.892 24.775 30.287 25.025 30.673 25.267 31.052 25.502 50 39.196 31.424 25.730 21.482 18.256 15.762

11.46911.65411.82612.13712.27812.40912.53212.64712.75412.85412.94813.03513.11713.19313.26513.33213.39413.45213.50713.55813.60613.65013.69213.73013.76713.801

7.282910.675 9.823 9.077 8.422 7.843 7.33007.371711.258 10.27411.655 10.56711.925 10.75712.108 10.88112.233 10.962

7.40867.44127.47019.427 8.694 8.055 7.4957

6.83516.87296.90616.93526.96076.98307.0027

6.43386.46416.49066.51356.53356.55096.5660

6.0971 5.7662 6.1772

20.707 18.327 9.644 8.855 8.176

9.779 8.951 8.244

9.863 9.008 8.283

9.915 9.042 8.304

复利现值系数表 年金现值表 复利现值系数表

复 利 现 值 系 数 表

-n

计算公式：f=(1+i)

期数 1 2 3 4 5 6 7 8 9

1%

2%

3%

4%

5%

6% 0.94340.89000.83960.79210.74730.70500.66510.62740.59190.55840.52680.49700.46880.44230.41730.39360.37140.35030.33050.3118

7% 0.93460.87340.81630.76290.71300.66630.62270.58200.54390.50830.47510.44400.41500.38780.36240.33870.31660.29590.27650.2584

8% 0.92590.85730.79380.73500.68060.63020.58350.54030.50020.46320.42890.39710.36770.34050.31520.29190.27030.25020.23170.2145

9% 0.91740.84170.77220.70840.64990.59630.54700.50190.46040.42240.38750.35550.32620.29920.27450.25190.23110.21200.19450.1784

10%

11%

12% 0.89290.79720.71180.63550.56740.50660.45230.40390.36060.32200.28750.25670.22920.20460.18270.16310.14560.13000.11610.1037

13% 0.88500.78310.69310.61330.54280.48030.42510.37620.33290.29460.26070.23070.20420.18070.15990.14150.12520.11080.09810.0868

14% 0.87720.76950.67500.59210.51940.45560.39960.35060.30750.26970.23660.20760.18210.15970.14010.12290.10780.09460.08290.0728

15% 0.86960.75610.65750.57180.49720.43230.37590.32690.28430.24720.21490.18690.16250.14130.12290.10690.09290.08080.07030.0611

16%

17%

0.9901 0.98040.9803 0.96120.9706 0.94230.9610 0.92380.9515 0.90570.9420 0.88800.9327 0.87060.9235 0.85350.9143 0.8368

0.9709 0.9615 0.95240.9426 0.9246 0.90700.9151 0.8890 0.86380.8885 0.8548 0.82270.8626 0.8219 0.78350.8375 0.7903 0.74620.8131 0.7599 0.71070.7894 0.7307 0.67680.7664 0.7026 0.64460.7441 0.6756 0.61390.7224 0.6496 0.58470.7014 0.6246 0.55680.6810 0.6006 0.53030.6611 0.5775 0.50510.6419 0.5553 0.48100.6232 0.5339 0.45810.6050 0.5134 0.43630.5874 0.4936 0.41550.5703 0.4746 0.39570.5537 0.4564 0.3769

0.9091 0.90090.8264 0.81160.7513 0.73120.6830 0.65870.6209 0.59350.5645 0.53460.5132 0.48170.4665 0.43390.4241 0.39090.3855 0.35220.3505 0.31730.3186 0.28580.2897 0.25750.2633 0.23200.2394 0.20900.2176 0.18830.1978 0.16960.1799 0.15280.1635 0.13770.1486 0.1240

0.8621 0.8547 0.7432 0.7305 0.6407 0.6244 0.5523 0.5337 0.4761 0.4561 0.4104 0.3898 0.3538 0.3332 0.3050 0.2848 0.2630 0.2434 0.2267 0.2080 0.1954 0.1778 0.1685 0.1520 0.1452 0.1299 0.1252 0.1110 0.1079 0.0949 0.0930 0.0811 0.0802 0.0693 0.0691 0.0592 0.0596 0.0506 0.0514 0.0433

10 0.9053 0.820311 0.8963 0.804312 0.8874 0.788513 0.8787 0.773014 0.8700 0.757915 0.8613 0.743016 0.8528 0.728417 0.8444 0.714218 0.8360 0.700219 0.8277 0.686420 0.8195 0.6730

复利现值系数表 年金现值表 复利现值系数表

21 0.8114 0.659822 0.8034 0.646823 0.7954 0.634224 0.7876 0.621725 0.7798 0.609526 0.7720 0.597627 0.7644 0.585928 0.7568 0.574429 0.7493 0.563130 0.7419 0.5521

0.5375 0.4388 0.35890.5219 0.4220 0.34180.5067 0.4057 0.32560.4919 0.3901 0.31010.4776 0.3751 0.29530.4637 0.3607 0.28120.4502 0.3468 0.26780.4371 0.3335 0.25510.4243 0.3207 0.24290.4120 0.3083 0.2314

0.29420.27750.26180.24700.23300.21980.20740.19560.18460.1741

0.24150.22570.21090.19710.18420.17220.16090.15040.14060.1314

0.19870.18390.17030.15770.14600.13520.12520.11590.10730.0994

0.16370.15020.13780.12640.11600.10640.09760.08950.08220.0754

0.1351 0.11170.1228 0.10070.1117 0.09070.1015 0.08170.0923 0.07360.0839 0.06630.0763 0.05970.0693 0.05380.0630 0.04850.0573 0.0437

0.09260.08260.07380.06590.05880.05250.04690.04190.03740.0334

0.07680.06800.06010.05320.04710.04170.03690.03260.02890.0256

0.06380.05600.04910.04310.03780.03310.02910.02550.02240.0196

0.05310.04620.04020.03490.03040.02640.02300.02000.01740.0151

0.0443 0.0370 0.0382 0.0316 0.0329 0.0270 0.0284 0.0231 0.0245 0.0197 0.0211 0.0169 0.0182 0.0144 0.0157 0.0123 0.0135 0.0105 0.0116 0.0090

二 : 年金现值表 复利现值系数表

年金现值表

-n

计算公式：P=A*(P/A，i，n)=A*[1-（1＋i） ]/i，其中(P/A，i，n)称作“年金现值系数”

期数 1 2 3 4 5 6 7 8 9

1.0%

2.0%

3.0%

4.0%

14% 0.87721.64672.32162.91373.43313.88874.28834.63894.94645.21615.45275.66035.84246.00216.14226.26516.37296.46746.55046.62316.68706.74296.7921

0.86961.62572.28322.85503.35223.78454.16044.48734.77165.01885.23375.42065.58315.72455.84745.95426.04726.12806.19826.25936.31256.35876.3988

3.2743 3.1993 4.8332 4.6586 5.5755 5.3242 5.9288 5.6278 0.990 0.980 1.970 1.942 2.941 2.884 3.902 3.808 4.583 4.713 5.795 5.601 6.728 6.472 7.652 7.325 8.566 8.162

0.971 0.962 0.88501.913 1.886 1.66812.829 2.775 2.36123.717 3.630 2.97454.580 4.452 4.329 4.212 4.100 3.993 3.890 3.791 3.696 3.605 3.51725.417 5.242 3.99756.230 6.002 4.42267.020 6.733 4.79887.786 7.435 5.13178.530 8.111 7.722 7.360 7.024 6.710 6.418 6.145 5.889 5.650 5.42629.253 8.760 5.68699.954 9.385 5.9176

9.986 6.1218

10 9.471 8.983 9.787 10.575

11.348 10.635

12.106 11.296 6.302515 13.865 12.849 11.938 11.118 10.380 9.712 9.108 8.559 8.061 7.606 7.191 6.811 6.462413.578 12.561 10.10614.292 13.166 10.47714.992 13.754 6.60396.729110.059

6.83996.93809.818 9.129 8.514 7.963 7.469 7.02487.10167.16957.2297

15.678 14.324 20 18.046 16.351 14.877 13.590 12.462 11.470 10.59417.011 15.415 17.658 15.937 18.292 16.444 11.06111.272

18.914 16.936 25 22.023 19.523 17.413 15.622 14.094 12.78320.121 17.877 21.281 18.764 21.844 19.188 30 25.808 22.396 19.600 17.292 15.372 13.76522.938 20.000 23.468 20.389 23.989 20.766 24.499 21.132 35 29.409 24.999 21.487 18.665 16.374 14.49825.489 21.832 25.969 22.167 26.441 22.492 26.903 22.808 40 32.835 27.355 23.115 19.793 17.159 15.04627.799 23.412 28.235 23.701 28.662 23.982 29.080 24.254 45 36.095 29.490 24.519 20.720 17.774 15.45629.892 24.775 30.287 25.025 30.673 25.267 31.052 25.502 50 39.196 31.424 25.730 21.482 18.256 15.762

11.46911.65411.82612.13712.27812.40912.53212.64712.75412.85412.94813.03513.11713.19313.26513.33213.39413.45213.50713.55813.60613.65013.69213.73013.76713.801

7.282910.675 9.823 9.077 8.422 7.843 7.33007.371711.258 10.27411.655 10.56711.925 10.75712.108 10.88112.233 10.962

7.40867.44127.47019.427 8.694 8.055 7.4957

6.83516.87296.90616.93526.96076.98307.0027

6.43386.46416.49066.51356.53356.55096.5660

6.0971 5.7662 6.1772

20.707 18.327 9.644 8.855 8.176

9.779 8.951 8.244

9.863 9.008 8.283

9.915 9.042 8.304

复 利 现 值 系 数 表

-n

计算公式：f=(1+i)

期数 1 2 3 4 5 6 7 8 9

1%

2%

3%

4%

5%

6% 0.94340.89000.83960.79210.74730.70500.66510.62740.59190.55840.52680.49700.46880.44230.41730.39360.37140.35030.33050.3118

7% 0.93460.87340.81630.76290.71300.66630.62270.58200.54390.50830.47510.44400.41500.38780.36240.33870.31660.29590.27650.2584

8% 0.92590.85730.79380.73500.68060.63020.58350.54030.50020.46320.42890.39710.36770.34050.31520.29190.27030.25020.23170.2145

9% 0.91740.84170.77220.70840.64990.59630.54700.50190.46040.42240.38750.35550.32620.29920.27450.25190.23110.21200.19450.1784

10%

11%

12% 0.89290.79720.71180.63550.56740.50660.45230.40390.36060.32200.28750.25670.22920.20460.18270.16310.14560.13000.11610.1037

13% 0.88500.78310.69310.61330.54280.48030.42510.37620.33290.29460.26070.23070.20420.18070.15990.14150.12520.11080.09810.0868

14% 0.87720.76950.67500.59210.51940.45560.39960.35060.30750.26970.23660.20760.18210.15970.14010.12290.10780.09460.08290.0728

15% 0.86960.75610.65750.57180.49720.43230.37590.32690.28430.24720.21490.18690.16250.14130.12290.10690.09290.08080.07030.0611

16%

17%

0.9901 0.98040.9803 0.96120.9706 0.94230.9610 0.92380.9515 0.90570.9420 0.88800.9327 0.87060.9235 0.85350.9143 0.8368

0.9709 0.9615 0.95240.9426 0.9246 0.90700.9151 0.8890 0.86380.8885 0.8548 0.82270.8626 0.8219 0.78350.8375 0.7903 0.74620.8131 0.7599 0.71070.7894 0.7307 0.67680.7664 0.7026 0.64460.7441 0.6756 0.61390.7224 0.6496 0.58470.7014 0.6246 0.55680.6810 0.6006 0.53030.6611 0.5775 0.50510.6419 0.5553 0.48100.6232 0.5339 0.45810.6050 0.5134 0.43630.5874 0.4936 0.41550.5703 0.4746 0.39570.5537 0.4564 0.3769

0.9091 0.90090.8264 0.81160.7513 0.73120.6830 0.65870.6209 0.59350.5645 0.53460.5132 0.48170.4665 0.43390.4241 0.39090.3855 0.35220.3505 0.31730.3186 0.28580.2897 0.25750.2633 0.23200.2394 0.20900.2176 0.18830.1978 0.16960.1799 0.15280.1635 0.13770.1486 0.1240

0.8621 0.8547 0.7432 0.7305 0.6407 0.6244 0.5523 0.5337 0.4761 0.4561 0.4104 0.3898 0.3538 0.3332 0.3050 0.2848 0.2630 0.2434 0.2267 0.2080 0.1954 0.1778 0.1685 0.1520 0.1452 0.1299 0.1252 0.1110 0.1079 0.0949 0.0930 0.0811 0.0802 0.0693 0.0691 0.0592 0.0596 0.0506 0.0514 0.0433

10 0.9053 0.820311 0.8963 0.804312 0.8874 0.788513 0.8787 0.773014 0.8700 0.757915 0.8613 0.743016 0.8528 0.728417 0.8444 0.714218 0.8360 0.700219 0.8277 0.686420 0.8195 0.6730

21 0.8114 0.659822 0.8034 0.646823 0.7954 0.634224 0.7876 0.621725 0.7798 0.609526 0.7720 0.597627 0.7644 0.585928 0.7568 0.574429 0.7493 0.563130 0.7419 0.5521

0.5375 0.4388 0.35890.5219 0.4220 0.34180.5067 0.4057 0.32560.4919 0.3901 0.31010.4776 0.3751 0.29530.4637 0.3607 0.28120.4502 0.3468 0.26780.4371 0.3335 0.25510.4243 0.3207 0.24290.4120 0.3083 0.2314

0.29420.27750.26180.24700.23300.21980.20740.19560.18460.1741

0.24150.22570.21090.19710.18420.17220.16090.15040.14060.1314

0.19870.18390.17030.15770.14600.13520.12520.11590.10730.0994

0.16370.15020.13780.12640.11600.10640.09760.08950.08220.0754

0.1351 0.11170.1228 0.10070.1117 0.09070.1015 0.08170.0923 0.07360.0839 0.06630.0763 0.05970.0693 0.05380.0630 0.04850.0573 0.0437

0.09260.08260.07380.06590.05880.05250.04690.04190.03740.0334

0.07680.06800.06010.05320.04710.04170.03690.03260.02890.0256

0.06380.05600.04910.04310.03780.03310.02910.02550.02240.0196

0.05310.04620.04020.03490.03040.02640.02300.02000.01740.0151

0.0443 0.0370 0.0382 0.0316 0.0329 0.0270 0.0284 0.0231 0.0245 0.0197 0.0211 0.0169 0.0182 0.0144 0.0157 0.0123 0.0135 0.0105 0.0116 0.0090

三 : 年金现值系数和复利现金系数

首先说什么是年金，年金是每隔相等时间间隔收到或支付相同金额的款项，如每年年末收到养老金10000元，即为年金。年金现值系数公

式：P/A＝[1－（1+i）^-n]/i 其中i表示报酬率，n表示期数,P表示现值,A表示年金。比如你在银行里面每年年末存入1200元,年利率是10%的话

,你这5年所存入资金的现值=1200/(1+10%)+1200/(1+10%)^2+1200/(1+10%)^3+1200/(1+10%)^4+1200/(1+10%)^5

= 1200*[1- (1+10%)^ -5 ]/10%=1200*3.7908=4550 元。

1200元就是年金，4550就是年金现值，[1- (1+10%)^ -5 ]/10%=3.7908就是年金现值系数。复利现值系数是复利终值的对称概念，指未来一定时间的特定资金按复利计算的现在价值，或者说是为取得将来一定复利现值系数本利和现在所需要的本金。 复利现值的计算公式为：P=F*1/(1+i)^n，其中的1/(1+i)^n就是复利现值系数。记作（P/F，i,n），其中i是利率（折现率），n是年数。根据这两个条件就可以查到具体对应的复利现值系数了。说白了就是F=p*(1+i)^n的变形。复利终值与现值、普通年金终值与现值计算器

复利终值计算：

本金：

100

利率：

10.00%

计息期：

1

计算结果：

110

复利现值计算：

本金：

100

利率：

10.00%

计息期：

1

计算结果：

90.90909091

普通年金终值：

本金：

100

利率：

10.00%

计息期：

3

计算结果：

331

普通年金现值：

本金：

100

利率：

10.00%

计息期：

1

计算结果：

90.90909091

年金现值系数表的作用

要了解年金现值系数表的作用，首先要知道什么是年金现值系数。

所谓的年金，用通俗的说法来解释，就是每个相等的时间间隔发生一笔金额相同的款项流动，或支付或收到，例如，每年的年末都收到1万元，

这个就叫做年金。而年金现值，就是把这每一期发生的金额按照一定的系数折到现在，所加总的金额总额。

年金现值系数的计算公式是这样的：P/A=1/i -1/i(1+i)^n，其中，i是报酬率，n是期数，P是现值，A是年金。通过这个年金现值系数的公式，

带入相关的报酬率、期数、年金，就可以求现值了，同理，代入三个变量，就可以求出第四个变量。

根据年金现值系数公式，我们制定出了年金现值系数表。年金现值系数表是我们通过已知的报酬率、期数和年金求现值的的依据。年金现值

系数表的作用可以是：已知年金求现值、已知现值求年金、已知现值、年金和利率求期数和已知现值、年金和期数求利率。

四 : 年金现值系数与复利现值系数的关系

复利现值和年金现值之间的关系

复利现值和年金现值之间的关系：
它们的关系如下：（P/A,i,n）＝（1+i）-1+（1+i）-2+…+（1+i）-(n-1)+（1+i）-n
（P/F,i,n） =（1+i）-n
所以：
（P/A，10%，3）＝（P/F,10%,1）+（P/F,10%,2）+（P/F,10%,3）
＝（1＋10%）－3＋（1＋10%）－2＋（1＋10%）－1
＝0.7513＋0.8264＋0.9091＝2.4868。



针对该题常见的问题总结如下：

问题一：为什么三期复利现值系数相加就是第三期的年金现值系数，复利现值与年金现值之间是怎样的关系？
答复：利率为10%，3年期的年金现值系数＝（1＋10%）-3＋（1＋10%）-2＋（1＋10%）-1＝0.7513＋0.8264＋0.9091＝2.4868。


（1＋10%）-3表示的就是3期的复利现值系数。
（1＋10%）-2表示的就是2期的复利现值系数。
（1＋10%）-1表示的1期的复利现值系数。
所以三期复利现值系数相加就是第三期的年金现值系数。

复利现值和年金现值之间的关系，注意本题求的是普通年金的现值，不能直接套复利现值的公式，解释：
年金现值系数＝（P/A,i,n）＝（1+i）-1+（1+i）-2+…+（1+i）-(n-1)+（1+i）-n
复利现值系数＝（P/F,i,n） =（1+i）-n
所以：（P/A,i,n）＝（P/F,10%,1）+（P/F,10%,2）+（P/F,10%,3）+…+（P/F,i,n）
所以：
（P/A，10%，3）＝（P/F,10%,1）+（P/F,10%,2）+（P/F,10%,3）
＝（1＋10%）-3＋（1＋10%）-2＋（1＋10%）-1
＝0.7513＋0.8264＋0.9091＝2.4868。

问题三：已知（P/A,10%,4）=3.1699,（P/F,10%,4）=0.6830,（P/F,10%,5）=0.6209,则（P/A,10%,5）为:答案是3.7908,是（P/A,10%,4+,（P/F,10%,5）,是怎么转换的?
答复：根据教材的内容很容易知道：
（P/A，i，n）＝（1＋i）-1＋......＋（1＋i）-(n-1)＋（1＋i）-n
（P/A，i，n-1）＝（1＋i）-1＋......＋（1＋i）-（n-1）
即：（P/A，i，n）＝（P/A，i，n-1）＋（1＋i）-n
＝（P/A，i，n-1）＋（P/F，i，n）
所以，（P/A，10%，5）＝（P/A，10%，4）＋（P/F，10%，5）＝3.7908

问题四：n年的年金终值系数与n年的复利系数有什么样的关系？
答复：您好，n年的普通年金终值系数：(F/A,i,n)＝1+(1+i)+(1+i)2+…+(1+i)-(n-1)
＝1+(F/P，i，1)+(F/P，i，1)+…(F/P，i，n-2)+(F/P，i，n-1)
(F/P,i,n) =(1+i)n
所以说n期普通年金的终值系数等于n期的复利终值系数相加后除以(1+i)。 本文标题：复利年金现值系数表-年金现值表 复利现值系数表
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