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年金现值系数表完整版

年金现值系数,其英文名称为 “Present Value Interest Factor of Annuity”(PVIFA),是一个重要的财务概念。它用来估算一系列未来的定期支付在今天的总价值。这就好比你想知道,如果未来每年都能收到一定数额的钱,那么这些钱按照现在的货币价值总共值多少。

要计算年金现值系数,我们使用这样一个公式:

PVIFA = (1 – (1 + r)^(-n)) / r

这个公式中有两个关键变量:年利率(r)和期数(n)。年利率是指你的投资每年能带来的回报率,而期数则是指这样的投资会持续多少年。

这个公式的灵活之处在于它可以适应不同的支付频率。比如说,如果你每年收到一笔钱,那么就直接使用年利率和年数。但如果支付是每半年或者每月进行的,就需要对利率和期数做出调整。在半年支付的情况下,你需要将年利率换算成半年利率,并且将年数转换为半年的数量。同样的,如果是每月支付,利率就变为月利率,期数则是总共的月数。通过这种调整,无论支付频率如何,公式都能帮你准确计算出未来支付的当前总价值。

年金现值系数表 - 封面

下面是完整版的年金现值系数表:

表1: 利率r = 1%-5%, 期数n = 1-25

期数1%2%3%4%5%
10.99010.98040.97090.96150.9524
21.97041.94161.91351.88611.8594
32.94102.88392.82862.77512.7232
43.90203.80773.71713.62993.5460
54.85344.71354.57974.45184.3295
65.79555.60145.41725.24215.0757
76.72826.47206.23036.00215.7864
87.65177.32557.01976.73276.4632
98.56608.16227.78617.43537.1078
109.47138.98268.53028.11097.7217
1110.36769.78689.25268.76058.3064
1211.255110.57539.95409.38518.8633
1312.133711.348410.63509.98569.3936
1413.003712.106211.296110.56319.8986
1513.865112.849311.937911.118410.3797
1614.717913.577712.561111.652310.8378
1715.562314.291913.166112.165711.2741
1816.398314.992013.753512.659311.6896
1917.226015.678514.323813.133912.0853
2018.045616.351414.877513.590312.4622
2118.857017.011215.415014.029212.8212
2219.660417.658015.936914.451113.1630
2320.455818.292216.443614.856813.4886
2421.243418.913916.935515.247013.7986
2522.023219.523517.413115.622114.0939

表2: 利率r = 1%-5%, 期数n = 26-50

期数1%2%3%4%5%
2622.795220.121017.876815.982814.3752
2723.559620.706918.327016.329614.6430
2824.316421.281318.764116.663114.8981
2925.065821.844419.188516.983715.1411
3025.807722.396519.600417.292015.3725
3126.542322.937720.000417.588515.5928
3227.269623.468320.388817.873615.8027
3327.989723.988620.765818.147616.0025
3428.702724.498621.131818.411216.1929
3529.408624.998621.487218.664616.3742
3630.107525.488821.832318.908316.5469
3730.799525.969522.167219.142616.7113
3831.484726.440622.492519.367916.8679
3932.163026.902622.808219.584517.0170
4032.834727.355523.114819.792817.1591
4133.499727.799523.412419.993117.2944
4234.158128.234823.701420.185617.4232
4334.810028.661623.981920.370817.5459
4435.455529.080024.254320.548817.6628
4536.094529.490224.518720.720017.7741
4636.727229.892324.775420.884717.8801
4737.353730.286625.024721.042917.9810
4837.974030.673125.266721.195118.0772
4938.588131.052125.501721.341518.1687
5039.196131.423625.729821.482218.2559

表3: 利率r = 6%-10%, 期数n = 1-25

期数6%7%8%9%10%
10.94340.93460.92590.91740.9091
21.83341.80801.78331.75911.7355
32.67302.62432.57712.53132.4869
43.46513.38723.31213.23973.1699
54.21244.10023.99273.88973.7908
64.91734.76654.62294.48594.3553
75.58245.38935.20645.03304.8684
86.20985.97135.74665.53485.3349
96.80176.51526.24695.99525.7590
107.36017.02366.71016.41776.1446
117.88697.49877.13906.80526.4951
128.38387.94277.53617.16076.8137
138.85278.35777.90387.48697.1034
149.29508.74558.24427.78627.3667
159.71229.10798.55958.06077.6061
1610.10599.44668.85148.31267.8237
1710.47739.76329.12168.54368.0216
1810.827610.05919.37198.75568.2014
1911.158110.33569.60368.95018.3649
2011.469910.59409.81819.12858.5136
2111.764110.835510.01689.29228.6487
2212.041611.061210.20079.44248.7715
2312.303411.272210.37119.58028.8832
2412.550411.469310.52889.70668.9847
2512.783411.653610.67489.82269.0770

表4: 利率r = 6%-10%, 期数n = 26-50

期数6%7%8%9%10%
2613.003211.825810.81009.92909.1609
2713.210511.986710.935210.02669.2372
2813.406212.137111.051110.11619.3066
2913.590712.277711.158410.19839.3696
3013.764812.409011.257810.27379.4269
3113.929112.531811.349810.34289.4790
3214.084012.646611.435010.40629.5264
3314.230212.753811.513910.46449.5694
3414.368112.854011.586910.51789.6086
3514.498212.947711.654610.56689.6442
3614.621013.035211.717210.61189.6765
3714.736813.117011.775210.65309.7059
3814.846013.193511.828910.69089.7327
3914.949113.264911.878610.72559.7570
4015.046313.331711.924610.75749.7791
4115.138013.394111.967210.78669.7991
4215.224513.452412.006710.81349.8174
4315.306213.507012.043210.83809.8340
4415.383213.557912.077110.86059.8491
4515.455813.605512.108410.88129.8628
4615.524413.650012.137410.90029.8753
4715.589013.691612.164310.91769.8866
4815.650013.730512.189110.93369.8969
4915.707613.766812.212210.94829.9063
5015.761913.800712.233510.96179.9148

表5: 利率r = 11%-15%, 期数n = 1-25

期数11%12%13%14%15%
10.90090.89290.88500.87720.8696
21.71251.69011.66811.64671.6257
32.44372.40182.36122.32162.2832
43.10243.03732.97452.91372.8550
53.69593.60483.51723.43313.3522
64.23054.11143.99753.88873.7845
74.71224.56384.42264.28834.1604
85.14614.96764.79884.63894.4873
95.53705.32825.13174.94644.7716
105.88925.65025.42625.21615.0188
116.20655.93775.68695.45275.2337
126.49246.19445.91765.66035.4206
136.74996.42356.12185.84245.5831
146.98196.62826.30256.00215.7245
157.19096.81096.46246.14225.8474
167.37926.97406.60396.26515.9542
177.54887.11966.72916.37296.0472
187.70167.24976.83996.46746.1280
197.83937.36586.93806.55046.1982
207.96337.46947.02486.62316.2593
218.07517.56207.10166.68706.3125
228.17577.64467.16956.74296.3587
238.26647.71847.22976.79216.3988
248.34817.78437.28296.83516.4338
258.42177.84317.33006.87296.4641

表6: 利率r = 11%-15%, 期数n = 26-50

期数11%12%13%14%15%
268.48817.89577.37176.90616.4906
278.54787.94267.40866.93526.5135
288.60167.98447.44126.96076.5335
298.65018.02187.47016.98306.5509
308.69388.05527.49577.00276.5660
318.73318.08507.51837.01996.5791
328.76868.11167.53837.03506.5905
338.80058.13547.55607.04826.6005
348.82938.15667.57177.05996.6091
358.85528.17557.58567.07006.6166
368.87868.19247.59797.07906.6231
378.89968.20757.60877.08686.6288
388.91868.22107.61837.09376.6338
398.93578.23307.62687.09976.6380
408.95118.24387.63447.10506.6418
418.96498.25347.64107.10976.6450
428.97748.26197.64697.11386.6478
438.98868.26967.65227.11736.6503
448.99888.27647.65687.12056.6524
459.00798.28257.66097.12326.6543
469.01618.28807.66457.12566.6559
479.02358.29287.66777.12776.6573
489.03028.29727.67057.12966.6585
499.03628.30107.67307.13126.6596
509.04178.30457.67527.13276.6605

表7: 利率r = 16%-20%, 期数n = 1-25

期数16%17%18%19%20%
10.86210.85470.84750.84030.8333
21.60521.58521.56561.54651.5278
32.24592.20962.17432.13992.1065
42.79822.74322.69012.63862.5887
53.27433.19933.12723.05762.9906
63.68473.58923.49763.40983.3255
74.03863.92243.81153.70573.6046
84.34364.20724.07763.95443.8372
94.60654.45064.30304.16334.0310
104.83324.65864.49414.33894.1925
115.02864.83644.65604.48654.3271
125.19714.98844.79324.61054.4392
135.34235.11834.90954.71474.5327
145.46755.22935.00814.80234.6106
155.57555.32425.09164.87594.6755
165.66855.40535.16244.93774.7296
175.74875.47465.22234.98974.7746
185.81785.53395.27325.03334.8122
195.87755.58455.31625.07004.8435
205.92885.62785.35275.10094.8696
215.97315.66485.38375.12684.8913
226.01135.69645.40995.14864.9094
236.04425.72345.43215.16684.9245
246.07265.74655.45095.18224.9371
256.09715.76625.46695.19514.9476

表8: 利率r = 16%-20%, 期数n = 26-50

期数16%17%18%19%20%
266.11825.78315.48045.20604.9563
276.13645.79755.49195.21514.9636
286.15205.80995.50165.22284.9697
296.16565.82045.50985.22924.9747
306.17725.82945.51685.23474.9789
316.18725.83715.52275.23924.9824
326.19595.84375.52775.24304.9854
336.20345.84935.53205.24624.9878
346.20985.85415.53565.24894.9898
356.21535.85825.53865.25124.9915
366.22015.86175.54125.25314.9929
376.22425.86475.54345.25474.9941
386.22785.86735.54525.25614.9951
396.23095.86955.54685.25724.9959
406.23355.87135.54825.25824.9966
416.23585.87295.54935.25904.9972
426.23775.87435.55025.25964.9976
436.23945.87555.55105.26024.9980
446.24095.87655.55175.26074.9984
456.24215.87735.55235.26114.9986
466.24325.87815.55285.26144.9989
476.24425.87875.55325.26174.9991
486.24505.87925.55365.26194.9992
496.24575.87975.55395.26214.9993
506.24635.88015.55415.26234.9995

表9: 利率r = 21%-25%, 期数n = 1-25

期数21%22%23%24%25%
10.82640.81970.81300.80650.8000
21.50951.49151.47401.45681.4400
32.07392.04222.01141.98131.9520
42.54042.49362.44832.40432.3616
52.92602.86362.80352.74542.6893
63.24463.16693.09233.02052.9514
73.50793.41553.32703.24233.1611
83.72563.61933.51793.42123.3289
93.90543.78633.67313.56553.4631
104.05413.92323.79933.68193.5705
114.17694.03543.90183.77573.6564
124.27844.12743.98523.85143.7251
134.36244.20284.05303.91243.7801
144.43174.26464.10823.96163.8241
154.48904.31524.15304.00133.8593
164.53644.35674.18944.03333.8874
174.57554.39084.21904.05913.9099
184.60794.41874.24314.07993.9279
194.63464.44154.26274.09673.9424
204.65674.46034.27864.11033.9539
214.67504.47564.29164.12123.9631
224.69004.48824.30214.13003.9705
234.70254.49854.31064.13713.9764
244.71284.50704.31764.14283.9811
254.72134.51394.32324.14743.9849

表10: 利率r = 21%-25%, 期数n = 26-50

期数21%22%23%24%25%
264.72844.51964.32784.15113.9879
274.73424.52434.33164.15423.9903
284.73904.52814.33464.15663.9923
294.74304.53124.33714.15853.9938
304.74634.53384.33914.16013.9950
314.74904.53594.34074.16143.9960
324.75124.53764.34214.16243.9968
334.75314.53904.34314.16323.9975
344.75464.54024.34404.16393.9980
354.75594.54114.34474.16443.9984
364.75694.54194.34534.16493.9987
374.75784.54264.34584.16523.9990
384.75854.54314.34624.16553.9992
394.75914.54354.34654.16573.9993
404.75964.54394.34674.16593.9995
414.76004.54414.34694.16613.9996
424.76034.54444.34714.16623.9997
434.76064.54464.34724.16633.9997
444.76084.54474.34734.16633.9998
454.76104.54494.34744.16643.9998
464.76124.54504.34754.16653.9999
474.76134.54514.34764.16653.9999
484.76144.54514.34764.16653.9999
494.76154.54524.34774.16663.9999
504.76164.54524.34774.16663.9999

年金现值系数表使用案例

想象一下,如果你有一个机会,每年都能得到1000元,而这样的机会将持续10年。你可能会好奇,这些分散在未来10年的款项在当前的价值是多少。要解答这个问题,我们可以利用年金现值系数。

假设年利率为5%(即r=0.05),期数为10年(即n=10),我们可以通过公式计算出年金现值系数。或者,为了简便,我们也可以直接从上面的年金现值系数表中查找这个数值。在这个例子中,年金现值系数大约是7.7217。

下一步,我们将这个系数与每年收到的金额相乘。因此,年金的当前价值等于1000元(即每年的收入)乘以7.7217(年金现值系数),结果是7721.7元。这表示,按照5%的年利率计算,你每年收到1000元,持续10年的现金流,在今天的总价值相当于7721.7元。

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