年金現值

年金現值

年金現值就是在已知等額收付款金額未來本利(Future Value)、利率(interest)(這裡我們默認為年利率)和計息期數n時,考慮貨幣時間價值,計算出的這些收付款到現在的等價票面金額Present Value。

年金分為:普通年金(后付年金)、先付年金、遞延年金、永續年金徠等幾種。對應的,年金現值也可分為:普通年金現值、先付年金現值、遞延年金現值、永續年金現值。

分類


年金(Annuity)是指一定期間內每期等額收付的款項。因此,可以說年金是複利的產物,是複利的一種特殊形式(等額收付)
普通年金(Ordinary Annuity)是指 每期期末收付款項的年金,例如採用直線法計提的單項固定資產的折舊(折舊總額會隨著固定資產數量的變化而變化,不是年金,但就單項固定資產而言,其使用期內按直線法計提的折舊額是一定的)、一定期間的租金(租金不變期間)、每年員工的社會保險金(按月計算,每年7月1日到次年6月30日不變)、一定期間的貸款利息(即銀行存貸款利率不變且存貸金額不變期間,如貸款金額在銀行貸款利率不變期間有變化可以視為多筆年金)等。
先付年金(Annuity Due)是指 每期期初收付款項的年金,例如先付錢後用餐的餐廳,每一道菜(包括米飯、面、餃子和餛飩等)分別出來之後都是先付年金。
遞延年金(Deferred Annuity)是指在 預備計算時尚未發生收付,但 未來一定會發生若干期等額收付的年金,一般是在金融理財和社保回饋方面會產生遞延年金。遞延年金在做投資或其他資本預算時具有相當可觀的作用。
永續年金(Perpetual Annuity)即 無限期連續收付款的年金,最典型的就是諾貝爾獎金。

計算


普通年金現值

普通年金現值是以計算期期末為基準,在給定投資報酬率下按照貨幣時間價值計算出的未來一段期間內每年或每月收取或給付的年金現金流的折現值之和。類似普通年金終值,計算普通年金現值時,同樣要考慮到現金流是期初年金還是期末年金。
例如:某公司租用某設備,每年年末需要支付租金100元,年利率為10%,問5年內應支付的租金總額的現值是多少?
公式推導如下:
兩邊同時乘以 得兩式作差得
最後兩邊同時除以i得到公式。
如果年金的期數n很多,用上述方法計算現值顯然相當繁瑣。由於每年支付額相等,折算現值的係數又是有規律的,所以,可找出簡便的計算方法。
設每年的收付金額為A,利率為i,期數為n,則按複利計算的年金現值P為:
式中,稱為“年金現值係數”,記作,可查普通年金現值係數表。

先付年金現值

先付年金現值:是其最後一期期末時的本利和,相當於各期期初等額收付款項的複利現值之和。
n期先付年金與n期普通年金的收付款次數相同,但由於付款時間不同,n期先付年金現值比n期普通年金的現值多計算一期利息。因此在n期普通年金現值的基礎上乘以(1+i)而將分母加1就得出n期先付年金的現值了,公式為:
記作P(A,i,n)=
則如果上例為每年初計息的話,經過5年,逐年的現值為年金現值,計算為:

遞延年金現值

遞延年金終值,它的計算完全可以利用普通年金終值公式來計算(因為遞延期內沒有年金)

永續年金現值

永續年金因為是無限期收付的,所以其計算公式反而簡單,是
也徠就是說,如果這筆十萬美元投資是一筆專項基金的話,其永續現值為(美元)

係數表


1%~5%
年金現值係數表 
利率 —— 期間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
1715.562314.291913.166112.165711.2740
1816.398314.992013.753512.659311.6896
1917.226015.678514.323813.134012.0853
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
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
3630.107625.488821.832318.908316.5469
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
4938.588131.052125.501721.341418.1687
5039.196131.423625.729821.482218.2559
6%~10%
年金現值係數表
利率 —— 期數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
64.91734.76654.62284.48594.3553
75.58245.38935.20645.03304.8684
86.20985.97135.74665.53485.3349
96.80176.51526.24695.99525.7590
107.36017.02366.71016.41766.1446
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
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
4215.224513.452412.006710.81339.8174
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
4815.650013.730512.189210.93369.8969
4915.707613.766812.212210.94829.9063
5015.761913.800712.233510.96179.9148
11%~15%
年金現值係數表 
利率 —— 期數11%12%13%14%15%
10.90090.89290.88500.87720.8696
21.71251.69011.66811.64661.6257
32.44372.40182.36122.32162.2832
43.10243.03732.97452.91372.8550
53.69583.60483.51723.43313.3522
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
197.83937.36576.93806.55046.1982
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
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
328.76868.11167.53827.03506.5905
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
16%~20%
年金現值係數表 
利率 —— 期數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
215.97315.66475.38375.12684.8913
226.01135.69645.40995.14864.9094
236.04425.72345.43215.16684.9245
246.07265.74655.45095.18224.9371
256.09715.76625.46695.19514.9475
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
326.19585.84375.52775.24304.9854
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
21%~25%
年金現值係數表
利率 —— 期數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
204.65664.46034.27864.11033.9539
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
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
394.75904.54354.34654.16573.9993
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
454.76104.54484.34744.16643.9998
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
26%~30%
年金現值係數表 
利率 —— 期數26%27%28%29%30%
10.79370.78740.78130.77520.7692
21.42351.40741.39161.37611.3609
31.92341.89561.86841.84201.8161
42.32022.28002.24102.20312.1662
52.63512.58272.53202.48302.4356
62.88502.82102.75942.70002.6427
73.08333.00872.93702.86822.8021
83.24073.15643.07582.99862.9247
93.36573.27283.18423.09973.0190
103.46483.36443.26893.17803.0915
113.54353.43653.33513.23883.1473
123.60593.49333.38683.28593.1903
133.65553.53813.42723.32243.2233
143.69493.57333.45873.35073.2487
153.72613.60103.48343.37263.2682
163.75093.62283.50263.38963.2832
173.77053.64003.51773.40283.2948
183.78613.65363.52943.41303.3037
193.79853.66423.53863.42103.3105
203.80833.67263.54583.42713.3158
213.81613.67923.55143.43183.3198
223.82233.68443.55583.43563.3230
233.82733.68853.55923.43843.3254
243.83123.69183.56193.44063.3272
253.83423.69433.56403.44233.3286
263.83673.69633.56563.44373.3297
273.83873.69793.56693.44473.3306
283.84023.69913.56793.44553.3312
293.84143.70013.56873.44613.3317
303.84243.70093.56933.44663.3321
313.84323.70153.56973.44703.3324
323.84383.70193.57013.44733.3326
333.84433.70233.57043.44753.3328
343.84473.70263.57063.44773.3329
353.84503.70283.57083.44783.3330
363.84523.70303.57093.44793.3331
373.84543.70323.57103.44803.3331
383.84563.70333.57113.44813.3332
393.84573.70343.57123.44813.3332
403.84583.70343.57123.44813.3332
413.84593.70353.57133.44823.3333
423.84593.70353.57133.44823.3333
433.84603.70363.57133.44823.3333
443.84603.70363.57143.44823.3333
453.84603.70363.57143.44823.3333
463.84613.70363.57143.44823.3333
473.84613.70373.57143.44833.3333
483.84613.70373.57143.44833.3333
493.84613.70373.57143.44833.3333
503.84613.70373.57143.44833.3333
31%~35%
年金現值係數表
利率 —— 期數31%32%33%34%35%
10.76340.75760.75190.74630.7407
21.34611.33151.31721.30321.2894
31.79091.76631.74231.71881.6959
42.13052.09572.06182.02901.9969
52.38972.34522.30212.26042.2200
62.58752.53422.48282.43312.3852
72.73862.67752.61872.56202.5075
82.85392.78602.72082.65822.5982
92.94192.86812.79762.73002.6653
103.00912.93042.85532.78362.7150
113.06042.97762.89872.82362.7519
123.09953.01332.93132.85342.7792
133.12943.04042.95592.87572.7994
143.15223.06092.97442.89232.8144
153.16963.07642.98832.90472.8255
163.18293.08822.99872.91402.8337
173.19313.09713.00652.92092.8398
183.20083.10393.01242.92602.8443
193.20673.10903.01692.92992.8476
203.21123.11293.02022.93272.8501
213.21473.11583.02272.93492.8519
223.21733.11803.02462.93652.8533
233.21933.11973.02602.93772.8543
243.22093.12103.02712.93862.8550
253.22203.12203.02792.93922.8556
263.22293.12273.02852.93972.8560
273.22363.12333.02892.94012.8563
283.22413.12373.02932.94042.8565
293.22453.12403.02952.94062.8567
303.22483.12423.02972.94072.8568
313.22513.12443.02992.94082.8569
323.22523.12463.03002.94092.8569
333.22543.12473.03012.94102.8570
343.22553.12483.03012.94102.8570
353.22563.12483.03022.94112.8571
363.22563.12493.03022.94112.8571
373.22573.12493.03022.94112.8571
383.22573.12493.03022.94112.8571
393.22573.12493.03032.94112.8571
403.22573.12503.03032.94122.8571
413.22583.12503.03032.94122.8571
423.22583.12503.03032.94122.8571
433.22583.12503.03032.94122.8571
443.22583.12503.03032.94122.8571
453.22583.12503.03032.94122.8571
463.22583.12503.03032.94122.8571
473.22583.12503.03032.94122.8571
483.22583.12503.03032.94122.8571
493.22583.12503.03032.94122.8571
503.22583.12503.03032.94122.8571
36%~40%
年金現值信息表 
利率 —— 期數36%37%38%39%40%
10.73530.72990.72460.71940.7143
21.27601.26271.24971.23701.2245
31.67351.65161.63021.60931.5889
41.96581.93551.90601.87721.8492
52.18082.14272.10582.06992.0352
62.33882.29392.25062.20862.1680
72.45502.40432.35552.30832.2628
82.54042.48492.43152.38012.3306
92.60332.54372.48662.43172.3790
102.64952.58672.52652.46892.4136
112.68342.61802.55552.49562.4383
122.70842.64092.57642.51482.4559
132.72682.65762.59162.52862.4685
142.74032.66982.60262.53862.4775
152.75022.67872.61062.54572.4839
162.75752.68522.61642.55092.4885
172.76292.68992.62062.55462.4918
182.76682.69342.62362.55732.4941
192.76972.69592.62582.55922.4958
202.77182.69772.62742.56062.4970
212.77342.69912.62862.56162.4979
222.77462.70002.62942.56232.4985
232.77542.70082.63002.56282.4989
242.77602.70132.63042.56322.4992
252.77652.70172.63072.56342.4994
262.77682.70192.63102.56362.4996
272.77712.70222.63112.56372.4997
282.77732.70232.63132.56382.4998
292.77742.70242.63132.56392.4999
302.77752.70252.63142.56402.4999
312.77762.70252.63152.56402.4999
322.77762.70262.63152.56402.4999
332.77772.70262.63152.56412.5000
342.77772.70262.63152.56412.5000
352.77772.70272.63152.56412.5000
362.77772.70272.63162.56412.5000
372.77772.70272.63162.56412.5000
382.77782.70272.63162.56412.5000
392.77782.70272.63162.56412.5000
402.77782.70272.63162.56412.5000
412.77782.70272.63162.56412.5000
422.77782.70272.63162.56412.5000
432.77782.70272.63162.56412.5000
442.77782.70272.63162.56412.5000
452.77782.70272.63162.56412.5000
462.77782.70272.63162.56412.5000
472.77782.70272.63162.56412.5000
482.77782.70272.63162.56412.5000
492.77782.70272.63162.56412.5000
502.77782.70272.63162.56412.5000
41%~45%
年金現值係數表
利率 —— 期數41%42%43%44%45%
10.70920.70420.69930.69440.6897
21.21221.20021.18831.17671.1652
31.56891.54941.53031.51161.4933
41.82191.79541.76941.74421.7195
52.00141.96861.93671.90571.8755
62.12862.09052.05362.01781.9831
72.21892.17642.13542.09572.0573
82.28292.23692.19262.14982.1085
92.32832.27952.23262.18742.1438
102.36052.30952.26052.21342.1681
112.38332.33072.28012.23162.1849
122.39952.34552.29382.24412.1965
132.41102.35602.30332.25292.2045
142.41922.36342.31002.25892.2100
152.42492.36862.31472.26322.2138
162.42902.37222.31802.26612.2164
172.43192.37482.32032.26812.2182
182.43402.37662.32192.26952.2195
192.43552.37792.32302.27052.2203
202.43652.37882.32382.27122.2209
212.43722.37942.32432.27172.2213
222.43772.37992.32472.27202.2216
232.43812.38022.32502.27222.2218
242.43842.38042.32512.27242.2219
252.43862.38062.32532.27252.2220
262.43872.38072.32542.27262.2221
272.43882.38082.32542.27262.2221
282.43892.38082.32552.27262.2222
292.43892.38092.32552.27272.2222
302.43892.38092.32552.27272.2222
312.43902.38092.32552.27272.2222
322.43902.38092.32562.27272.2222
332.43902.38092.32562.27272.2222
342.43902.38092.32562.27272.2222
352.43902.38092.32562.27272.2222
362.43902.38092.32562.27272.2222
372.43902.38092.32562.27272.2222
382.43902.38092.32562.27272.2222
392.43902.38092.32562.27272.2222
402.43902.38102.32562.27272.2222
412.43902.38102.32562.27272.2222
422.43902.38102.32562.27272.2222
432.43902.38102.32562.27272.2222
442.43902.38102.32562.27272.2222
452.43902.38102.32562.27272.2222
462.43902.38102.32562.27272.2222
472.43902.38102.32562.27272.2222
482.43902.38102.32562.27272.2222
492.43902.38102.32562.27272.2222
502.43902.38102.32562.27272.2222
46%~50%
年金現值係數表
利率 —— 期數46%47%48%49%50%
10.68490.68030.67570.67110.6667
21.15411.14301.13221.12161.1111
31.47541.45791.44071.42391.4074
41.69551.67201.64911.62681.6049
51.84621.81771.78991.76291.7366
61.94951.91681.88511.85431.8244
72.02021.98421.94941.91561.8829
82.06862.03011.99281.95681.9220
92.10182.06132.02221.98441.9480
102.12452.08252.04202.00301.9653
112.14012.09692.05542.01541.9769
122.15072.10682.06452.02371.9846
132.15802.11342.07062.02941.9897
142.16302.11802.07472.03311.9931
152.16652.12112.07752.03571.9954
162.16882.12322.07942.03741.9970
172.17042.12462.08072.03851.9980
182.17152.12562.08152.03931.9986
192.17232.12632.08212.03981.9991
202.17282.12672.08252.04011.9994
212.17312.12702.08282.04031.9996
222.17342.12722.08302.04051.9997
232.17362.12742.08312.04061.9998
242.17372.12752.08322.04071.9999
252.17372.12752.08322.04071.9999
262.17382.12762.08332.04081.9999
272.17382.12762.08332.04082.0000
282.17392.12762.08332.04082.0000
292.17392.12762.08332.04082.0000
302.17392.12762.08332.04082.0000
312.17392.12762.08332.04082.0000
322.17392.12772.08332.04082.0000
332.17392.12772.08332.04082.0000
342.17392.12772.08332.04082.0000
352.17392.12772.08332.04082.0000
362.17392.12772.08332.04082.0000
372.17392.12772.08332.04082.0000
382.17392.12772.08332.04082.0000
392.17392.12772.08332.04082.0000
402.17392.12772.08332.04082.0000
412.17392.12772.08332.04082.0000
422.17392.12772.08332.04082.0000
432.17392.12772.08332.04082.0000
442.17392.12772.08332.04082.0000
452.17392.12772.08332.04082.0000
462.17392.12772.08332.04082.0000
472.17392.12772.08332.04082.0000
482.17392.12772.08332.04082.0000
492.17392.12772.08332.04082.0000
502.17392.12772.08332.04082.0000

作用


計算貨幣價值

已知年金和係數,計算年金現值,得出某一時點貨幣的價值,這是年金現值的基本作用。

比較投資方案

根據貨幣價值的不同,可以比較投資方案/籌資方案的優劣。

比較方案優劣

不同年限、不同投資/籌資總額的方案可以通過計算年金凈現值(ANPV)指標進行方案優劣比較。

計算報酬率

通過插值法可以計算出籌資內含報酬率(IRR)。