普通年金现值是以计算期期末为基准,在给定投资报酬率下按照货币时间价值计算出的未来一段期间内每年或每月收取或给付的年金现金流的折现值之和。类似普通年金终值,计算普通年金现值时,同样要考虑到现金流是期初年金还是期末年金。例如:某公司租用某设备,每年年末需要支付租金100元,年利率为10%,问5年内应支付的租金总额的现值是多少?公式推导如下:两边同时乘以得两式作差得最后两边同时除以i得到公式。如果年金的期数n很多,用上述方法计算现值显然相当繁琐。由于每年支付额相等,折算现值的系数又是有规律的,所以,可找出简便的计算方法。设每年的收付金额为A,利率为i,期数为n,则按复利计算的年金现值P为:。式中,称为“年金现值系数”,记作(P/A,i,n),可查普通年金现值系数表。先付年金现值:是其最后一期期末时的本利和,相当于各期期初等额收付款项的复利现值之和。n期先付年金与n期普通年金的收付款次数相同,但由于付款时间不同,n期先付年金现值比n期普通年金的现值多计算一期利息。因此在n期普通年金现值的基础上乘以(1+i)而将分母加1就得出n期先付年金的现值了,公式为:记作P(A,i,n)=A·[(P/A,i,n-1)+1]则如果上例为每年初计息的话,经过5年,逐年的现值为年金现值,计算为:递延年金终值,它的计算完全可以利用普通年金终值公式来计算(因为递延期内没有年金)永续年金因为是无限期收付的,所以其计算公式反而简单,是也就是说,如果这笔十万美元投资是一笔专项基金的话,其永续现值为(美元)1%~5%年金现值系数表利率——期间1%2%3%4%5%10.99010.98040.97090.96150.952421.97041.94161.91351.88611.859432.94102.88392.82862.77512.723243.90203.80773.71713.62993.546054.85344.71354.57974.45184.329565.79555.60145.41725.24215.075776.72826.47206.23036.00215.786487.65177.32557.01976.73276.463298.56608.16227.78617.43537.1078109.47138.98268.53028.11097.72171110.36769.78689.25268.76058.30641211.255110.57539.95409.38518.86331312.133711.348410.63509.98569.39361413.003712.106211.296110.56319.89861513.865112.849311.937911.118410.37971614.717913.577712.561111.652310.83781715.562314.291913.166112.165711.27401816.398314.992013.753512.659311.68961917.226015.678514.323813.134012.08532018.045616.351414.877513.590312.46222118.857017.011215.415014.029212.82122219.660417.658015.936914.451113.16302320.455818.292216.443614.856813.48862421.243418.913916.935515.247013.79862522.023219.523517.413115.622114.09392622.795220.121017.876815.982814.37522723.559620.706918.327016.329614.64302824.316421.281318.764116.663114.89812925.065821.844419.188516.983715.14113025.807722.396519.600417.292015.37253126.542322.937720.000417.588515.59283227.269623.468320.388817.873615.80273327.989723.988620.765818.147616.00253428.702724.498621.131818.411216.19293529.408624.998621.487218.664616.37423630.107625.488821.832318.908316.54693730.799525.969522.167219.142616.71133831.484726.440622.492519.367916.86793932.163026.902622.808219.584517.01704032.834727.355523.114819.792817.15914133.499727.799523.412419.993117.29444234.158128.234823.701420.185617.42324334.810028.661623.981920.370817.54594435.455529.080024.254320.548817.66284536.094529.490224.518720.720017.77414636.727229.892324.775420.884717.88014737.353730.286625.024721.042917.98104837.974030.673125.266721.195118.07724938.588131.052125.501721.341418.16875039.196131.423625.729821.482218.25596%~10%年金现值系数表利率——期数6%7%8%9%10%10.94340.93460.92590.91740.909121.83341.80801.78331.75911.735532.67302.62432.57712.53132.486943.46513.38723.31213.23973.169954.21244.10023.99273.88973.790864.91734.76654.62284.48594.355375.58245.38935.20645.03304.868486.20985.97135.74665.53485.334996.80176.51526.24695.99525.7590107.36017.02366.71016.41766.1446117.88697.49877.13906.80526.4951128.38387.94277.53617.16076.8137138.85278.35777.90387.48697.1034149.29508.74558.24427.78627.3667159.71229.10798.55958.06077.60611610.10599.44668.85148.31267.82371710.47739.76329.12168.54368.02161810.827610.05919.37198.75568.20141911.158110.33569.60368.95018.36492011.469910.59409.81819.12858.51362111.764110.835510.01689.29228.64872212.041611.061210.20079.44248.77152312.303411.272210.37119.58028.88322412.550411.469310.52889.70668.98472512.783411.653610.67489.82269.07702613.003211.825810.81009.92909.16092713.210511.986710.935210.02669.23722813.406212.137111.051110.11619.30662913.590712.277711.158410.19839.36963013.764812.409011.257810.27379.42693113.929112.531811.349810.34289.47903214.084012.646611.435010.40629.52643314.230212.753811.513910.46449.56943414.368112.854011.586910.51789.60863514.498212.947711.654610.56689.64423614.621013.035211.717210.61189.67653714.736813.117011.775210.65309.70593814.846013.193511.828910.69089.73273914.949113.264911.878610.72559.75704015.046313.331711.924610.75749.77914115.138013.394111.967210.78669.79914215.224513.452412.006710.81339.81744315.306213.507012.043210.83809.83404415.383213.557912.077110.86059.84914515.455813.605512.108410.88129.86284615.524413.650012.137410.90029.87534715.589013.691612.164310.91769.88664815.650013.730512.189210.93369.89694915.707613.766812.212210.94829.90635015.761913.800712.233510.96179.914811%~15%年金现值系数表利率——期数11%12%13%14%15%10.90090.89290.88500.87720.869621.71251.69011.66811.64661.625732.44372.40182.36122.32162.283243.10243.03732.97452.91372.855053.69583.60483.51723.43313.352264.23054.11143.99753.88873.784574.71224.56384.42264.28834.160485.14614.96764.79884.63894.487395.53705.32825.13174.94644.7716105.88925.65025.42625.21615.0188116.20655.93775.68695.45275.2337126.49246.19445.91765.66035.4206136.74996.42356.12185.84245.5831146.98196.62826.30256.00215.7245157.19096.81096.46246.14225.8474167.37926.97406.60396.26515.9542177.54887.11966.72916.37296.0472187.70167.24976.83996.46746.1280197.83937.36576.93806.55046.1982207.96337.46947.02486.62316.2593218.07517.56207.10166.68706.3125228.17577.64467.16956.74296.3587238.26647.71847.22976.79216.3988248.34817.78437.28296.83516.4338258.42177.84317.33006.87296.4641268.48817.89577.37176.90616.4906278.54787.94267.40866.93526.5135288.60167.98447.44126.96076.5335298.65018.02187.47016.98306.5509308.69388.05527.49577.00276.5660318.73318.08507.51837.01996.5791328.76868.11167.53827.03506.5905338.80058.13547.55607.04826.6005348.82938.15667.57177.05996.6091358.85528.17557.58567.07006.6166368.87868.19247.59797.07906.6231378.89968.20757.60877.08686.6288388.91868.22107.61837.09376.6338398.93578.23307.62687.09976.6380408.95118.24387.63447.10506.6418418.96498.25347.64107.10976.6450428.97748.26197.64697.11386.6478438.98868.26967.65227.11736.6503448.99888.27647.65687.12056.6524459.00798.28257.66097.12326.6543469.01618.28807.66457.12566.6559479.02358.29287.66777.12776.6573489.03028.29727.67057.12966.6585499.03628.30107.67307.13126.6596509.04178.30457.67527.13276.660516%~20%年金现值系数表利率——期数16%17%18%19%20%10.86210.85470.84750.84030.833321.60521.58521.56561.54651.527832.24592.20962.17432.13992.106542.79822.74322.69012.63862.588753.27433.19933.12723.05762.990663.68473.58923.49763.40983.325574.03863.92243.81153.70573.604684.34364.20724.07763.95443.837294.60654.45064.30304.16334.0310104.83324.65864.49414.33894.1925115.02864.83644.65604.48654.3271125.19714.98844.79324.61054.4392135.34235.11834.90954.71474.5327145.46755.22935.00814.80234.6106155.57555.32425.09164.87594.6755165.66855.40535.16244.93774.7296175.74875.47465.22234.98974.7746185.81785.53395.27325.03334.8122195.87755.58455.31625.07004.8435205.92885.62785.35275.10094.8696215.97315.66475.38375.12684.8913226.01135.69645.40995.14864.9094236.04425.72345.43215.16684.9245246.07265.74655.45095.18224.9371256.09715.76625.46695.19514.9475266.11825.78315.48045.20604.9563276.13645.79755.49195.21514.9636286.15205.80995.50165.22284.9697296.16565.82045.50985.22924.9747306.17725.82945.51685.23474.9789316.18725.83715.52275.23924.9824326.19585.84375.52775.24304.9854336.20345.84935.53205.24624.9878346.20985.85415.53565.24894.9898356.21535.85825.53865.25124.9915366.22015.86175.54125.25314.9929376.22425.86475.54345.25474.9941386.22785.86735.54525.25614.9951396.23095.86955.54685.25724.9959406.23355.87135.54825.25824.9966416.23585.87295.54935.25904.9972426.23775.87435.55025.25964.9976436.23945.87555.55105.26024.9980446.24095.87655.55175.26074.9984456.24215.87735.55235.26114.9986466.24325.87815.55285.26144.9989476.24425.87875.55325.26174.9991486.24505.87925.55365.26194.9992496.24575.87975.55395.26214.9993506.24635.88015.55415.26234.999521%~25%年金现值系数表利率——期数21%22%23%24%25%10.82640.81970.81300.80650.800021.50951.49151.47401.45681.440032.07392.04222.01141.98131.952042.54042.49362.44832.40432.361652.92602.86362.80352.74542.689363.24463.16693.09233.02052.951473.50793.41553.32703.24233.161183.72563.61933.51793.42123.328993.90543.78633.67313.56553.4631104.05413.92323.79933.68193.5705114.17694.03543.90183.77573.6564124.27844.12743.98523.85143.7251134.36244.20284.05303.91243.7801144.43174.26464.10823.96163.8241154.48904.31524.15304.00133.8593164.53644.35674.18944.03333.8874174.57554.39084.21904.05913.9099184.60794.41874.24314.07993.9279194.63464.44154.26274.09673.9424204.65664.46034.27864.11033.9539214.67504.47564.29164.12123.9631224.69004.48824.30214.13003.9705234.70254.49854.31064.13713.9764244.71284.50704.31764.14283.9811254.72134.51394.32324.14743.9849264.72844.51964.32784.15113.9879274.73424.52434.33164.15423.9903284.73904.52814.33464.15663.9923294.74304.53124.33714.15853.9938304.74634.53384.33914.16013.9950314.74904.53594.34074.16143.9960324.75124.53764.34214.16243.9968334.75314.53904.34314.16323.9975344.75464.54024.34404.16393.9980354.75594.54114.34474.16443.9984364.75694.54194.34534.16493.9987374.75784.54264.34584.16523.9990384.75854.54314.34624.16553.9992394.75904.54354.34654.16573.9993404.75964.54394.34674.16593.9995414.76004.54414.34694.16613.9996424.76034.54444.34714.16623.9997434.76064.54464.34724.16633.9997444.76084.54474.34734.16633.9998454.76104.54484.34744.16643.9998464.76124.54504.34754.16653.9999474.76134.54514.34764.16653.9999484.76144.54514.34764.16653.9999494.76154.54524.34774.16663.9999504.76164.54524.34774.16663.999926%~30%年金现值系数表利率——期数26%27%28%29%30%10.79370.78740.78130.77520.769221.42351.40741.39161.37611.360931.92341.89561.86841.84201.816142.32022.28002.24102.20312.166252.63512.58272.53202.48302.435662.88502.82102.75942.70002.642773.08333.00872.93702.86822.802183.24073.15643.07582.99862.924793.36573.27283.18423.09973.0190103.46483.36443.26893.17803.0915113.54353.43653.33513.23883.1473123.60593.49333.38683.28593.1903133.65553.53813.42723.32243.2233143.69493.57333.45873.35073.2487153.72613.60103.48343.37263.2682163.75093.62283.50263.38963.2832173.77053.64003.51773.40283.2948183.78613.65363.52943.41303.3037193.79853.66423.53863.42103.3105203.80833.67263.54583.42713.3158213.81613.67923.55143.43183.3198223.82233.68443.55583.43563.3230233.82733.68853.55923.43843.3254243.83123.69183.56193.44063.3272253.83423.69433.56403.44233.3286263.83673.69633.56563.44373.3297273.83873.69793.56693.44473.3306283.84023.69913.56793.44553.3312293.84143.70013.56873.44613.3317303.84243.70093.56933.44663.3321313.84323.70153.56973.44703.3324323.84383.70193.57013.44733.3326333.84433.70233.57043.44753.3328343.84473.70263.57063.44773.3329353.84503.70283.57083.44783.3330363.84523.70303.57093.44793.3331373.84543.70323.57103.44803.3331383.84563.70333.57113.44813.3332393.84573.70343.57123.44813.3332403.84583.70343.57123.44813.3332413.84593.70353.57133.44823.3333423.84593.70353.57133.44823.3333433.84603.70363.57133.44823.3333443.84603.70363.57143.44823.3333453.84603.70363.57143.44823.3333463.84613.70363.57143.44823.3333473.84613.70373.57143.44833.3333483.84613.70373.57143.44833.3333493.84613.70373.57143.44833.3333503.84613.70373.57143.44833.333331%~35%年金现值系数表利率——期数31%32%33%34%35%10.76340.75760.75190.74630.740721.34611.33151.31721.30321.289431.79091.76631.74231.71881.695942.13052.09572.06182.02901.996952.38972.34522.30212.26042.220062.58752.53422.48282.43312.385272.73862.67752.61872.56202.507582.85392.78602.72082.65822.598292.94192.86812.79762.73002.6653103.00912.93042.85532.78362.7150113.06042.97762.89872.82362.7519123.09953.01332.93132.85342.7792133.12943.04042.95592.87572.7994143.15223.06092.97442.89232.8144153.16963.07642.98832.90472.8255163.18293.08822.99872.91402.8337173.19313.09713.00652.92092.8398183.20083.10393.01242.92602.8443193.20673.10903.01692.92992.8476203.21123.11293.02022.93272.8501213.21473.11583.02272.93492.8519223.21733.11803.02462.93652.8533233.21933.11973.02602.93772.8543243.22093.12103.02712.93862.8550253.22203.12203.02792.93922.8556263.22293.12273.02852.93972.8560273.22363.12333.02892.94012.8563283.22413.12373.02932.94042.8565293.22453.12403.02952.94062.8567303.22483.12423.02972.94072.8568313.22513.12443.02992.94082.8569323.22523.12463.03002.94092.8569333.22543.12473.03012.94102.8570343.22553.12483.03012.94102.8570353.22563.12483.03022.94112.8571363.22563.12493.03022.94112.8571373.22573.12493.03022.94112.8571383.22573.12493.03022.94112.8571393.22573.12493.03032.94112.8571403.22573.12503.03032.94122.8571413.22583.12503.03032.94122.8571423.22583.12503.03032.94122.8571433.22583.12503.03032.94122.8571443.22583.12503.03032.94122.8571453.22583.12503.03032.94122.8571463.22583.12503.03032.94122.8571473.22583.12503.03032.94122.8571483.22583.12503.03032.94122.8571493.22583.12503.03032.94122.8571503.22583.12503.03032.94122.857136%~40%年金现值信息表利率——期数36%37%38%39%40%10.73530.72990.72460.71940.714321.27601.26271.24971.23701.224531.67351.65161.63021.60931.588941.96581.93551.90601.87721.849252.18082.14272.10582.06992.035262.33882.29392.25062.20862.168072.45502.40432.35552.30832.262882.54042.48492.43152.38012.330692.60332.54372.48662.43172.3790102.64952.58672.52652.46892.4136112.68342.61802.55552.49562.4383122.70842.64092.57642.51482.4559132.72682.65762.59162.52862.4685142.74032.66982.60262.53862.4775152.75022.67872.61062.54572.4839162.75752.68522.61642.55092.4885172.76292.68992.62062.55462.4918182.76682.69342.62362.55732.4941192.76972.69592.62582.55922.4958202.77182.69772.62742.56062.4970212.77342.69912.62862.56162.4979222.77462.70002.62942.56232.4985232.77542.70082.63002.56282.4989242.77602.70132.63042.56322.4992252.77652.70172.63072.56342.4994262.77682.70192.63102.56362.4996272.77712.70222.63112.56372.4997282.77732.70232.63132.56382.4998292.77742.70242.63132.56392.4999302.77752.70252.63142.56402.4999312.77762.70252.63152.56402.4999322.77762.70262.63152.56402.4999332.77772.70262.63152.56412.5000342.77772.70262.63152.56412.5000352.77772.70272.63152.56412.5000362.77772.70272.63162.56412.5000372.77772.70272.63162.56412.5000382.77782.70272.63162.56412.5000392.77782.70272.63162.56412.5000402.77782.70272.63162.56412.5000412.77782.70272.63162.56412.5000422.77782.70272.63162.56412.5000432.77782.70272.63162.56412.5000442.77782.70272.63162.56412.5000452.77782.70272.63162.56412.5000462.77782.70272.63162.56412.5000472.77782.70272.63162.56412.5000482.77782.70272.63162.56412.5000492.77782.70272.63162.56412.5000502.77782.70272.63162.56412.500041%~45%年金现值系数表利率——期数41%42%43%44%45%10.70920.70420.69930.69440.689721.21221.20021.18831.17671.165231.56891.54941.53031.51161.493341.82191.79541.76941.74421.719552.00141.96861.93671.90571.875562.12862.09052.05362.01781.983172.21892.17642.13542.09572.057382.28292.23692.19262.14982.108592.32832.27952.23262.18742.1438102.36052.30952.26052.21342.1681112.38332.33072.28012.23162.1849122.39952.34552.29382.24412.1965132.41102.35602.30332.25292.2045142.41922.36342.31002.25892.2100152.42492.36862.31472.26322.2138162.42902.37222.31802.26612.2164172.43192.37482.32032.26812.2182182.43402.37662.32192.26952.2195192.43552.37792.32302.27052.2203202.43652.37882.32382.27122.2209212.43722.37942.32432.27172.2213222.43772.37992.32472.27202.2216232.43812.38022.32502.27222.2218242.43842.38042.32512.27242.2219252.43862.38062.32532.27252.2220262.43872.38072.32542.27262.2221272.43882.38082.32542.27262.2221282.43892.38082.32552.27262.2222292.43892.38092.32552.27272.2222302.43892.38092.32552.27272.2222312.43902.38092.32552.27272.2222322.43902.38092.32562.27272.2222332.43902.38092.32562.27272.2222342.43902.38092.32562.27272.2222352.43902.38092.32562.27272.2222362.43902.38092.32562.27272.2222372.43902.38092.32562.27272.2222382.43902.38092.32562.27272.2222392.43902.38092.32562.27272.2222402.43902.38102.32562.27272.2222412.43902.38102.32562.27272.2222422.43902.38102.32562.27272.2222432.43902.38102.32562.27272.2222442.43902.38102.32562.27272.2222452.43902.38102.32562.27272.2222462.43902.38102.32562.27272.2222472.43902.38102.32562.27272.2222482.43902.38102.32562.27272.2222492.43902.38102.32562.27272.2222502.43902.38102.32562.27272.222246%~50%年金现值系数表利率——期数46%47%48%49%50%10.68490.68030.67570.67110.666721.15411.14301.13221.12161.111131.47541.45791.44071.42391.407441.69551.67201.64911.62681.604951.84621.81771.78991.76291.736661.94951.91681.88511.85431.824472.02021.98421.94941.91561.882982.06862.03011.99281.95681.922092.10182.06132.02221.98441.9480102.12452.08252.04202.00301.9653112.14012.09692.05542.01541.9769122.15072.10682.06452.02371.9846132.15802.11342.07062.02941.9897142.16302.11802.07472.03311.9931152.16652.12112.07752.03571.9954162.16882.12322.07942.03741.9970172.17042.12462.08072.03851.9980182.17152.12562.08152.03931.9986192.17232.12632.08212.03981.9991202.17282.12672.08252.04011.9994212.17312.12702.08282.04031.9996222.17342.12722.08302.04051.9997232.17362.12742.08312.04061.9998242.17372.12752.08322.04071.9999252.17372.12752.08322.04071.9999262.17382.12762.08332.04081.9999272.17382.12762.08332.04082.0000282.17392.12762.08332.04082.0000292.17392.12762.08332.04082.0000302.17392.12762.08332.04082.0000312.17392.12762.08332.04082.0000322.17392.12772.08332.04082.0000332.17392.12772.08332.04082.0000342.17392.12772.08332.04082.0000352.17392.12772.08332.04082.0000362.17392.12772.08332.04082.0000372.17392.12772.08332.04082.0000382.17392.12772.08332.04082.0000392.17392.12772.08332.04082.0000402.17392.12772.08332.04082.0000412.17392.12772.08332.04082.0000422.17392.12772.08332.04082.0000432.17392.12772.08332.04082.0000442.17392.12772.08332.04082.0000452.17392.12772.08332.04082.0000462.17392.12772.08332.04082.0000472.17392.12772.08332.04082.0000482.17392.12772.08332.04082.0000492.17392.12772.08332.04082.0000502.17392.12772.08332.04082.0000