标题：年金终值
年金终值分类
年金按其每次收付发生的时点不同，可分为：普通年金（后付年金）、先付年金、递延年金、永续年金等几种，故年金终值亦可分为：普通年金终值、先付年金终值、递延年金终值。（注！永续年金只有现值，不存在终值。）普通年金终值普通年金终值：指一定时期内，每期期末等额收入或支出的本利和，也就是将每一期的金额，按复利换算到最后一期期末的终值，然后加总，就是该年金终值.例如：每年存款1元，年利率为10%，经过5年，逐年的终值和年金终值，公式为：F=A[(1+i)^n-1]/i，记作F=A（F/A，i，n）。推导如下： 
一年年末存1元
2年年末的终值=1*(1+10%)=(1+10%)
2年年末存入一元
3年年末的终值=1*(1+10%)^2+1*(1+10%)=(1+10%)^2+(1+10%)
3年年末存入一元
4年年末的终值=1*(1+10%)^3+1*(1+10%)^2+1*(1+10%)=(1+10%)^3+(1+10%)^2+(1+10%)
4年年末存入一元
5年年末的终值=1*(1+10%)^4+1*(1+10%)^3+1*(1+10%)^2+1*(1+10%)=(1+10%)^4+(1+10%)^3+(1+10%)^2+(1+10%)
5年年末存入一元
年金终值F=(1+10%)^4+(1+10%)^3+(1+10%)^2+(1+10%)+1
如果年金的期数很多，用上述方法计算终值显然相当繁琐.由于每年支付额相等，折算终值的系数又是有规律的，所以，可找出简便的计算方法.
设每年的支付金额为A，利率为i，期数为n，则按复利计算的年金终值F为：
F=A+A×(1+i)^1+…+A×(1+i)^(n-1)，　　　　　　　　
等比数列的求和公式
F=A[1-(1+i)^n]/[1-(1+i)]
F=A[1-(1+i)^n]/[1-1-i]
F=A[(1+i)^n-1]/i
式中[(1+i)^n-1]/i的为普通年金终值系数、或后付年金终值系数，利率为i，经过n期的年金终值记作(F/A，i,n),可查普通年金终值系数表.先付年金终值先付年金终值：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终值之和。
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期先付年金终值比n期普通年金的终值多计算一期利息。因此在n期普通年金终值的基础上乘以（1+i）就得出n期先付年金的终值了，公式为：
F=A{[[(1+i)^n]-1]/i}×(1+i)  或者F=A（【{[(1+i)^n+i]-i}/i】-1），记作F=A.[(F/A，i，n+1)-1]递延年金终值递延年金终值，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）
年金终值系数表
表 格 名 称： 年 金 终 值 系 数 表
计算公式：f=(1+i)n-1 i期数1%2%3%4%5%6%7%8%9%10%11%12%13%14%15%16%17%18%19%20%21%22%23%24%25%26%27%28%29%30%11.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000022.01002.02002.03002.04002.05002.06002.07002.08002.09002.10002.11002.12002.13002.14002.15002.16002.17002.18002.19002.20002.21002.22002.23002.24002.25002.26002.27002.28002.29002.300033.03013.06043.09093.12163.15253.18363.21493.24643.27813.31003.34213.37443.40693.43963.47253.50563.53893.57243.60613.64003.67413.70843.74293.77763.81253.84763.88293.91843.95413.990044.06044.12164.18364.24654.31014.37464.43994.50614.57314.64104.70974.77934.84984.92114.99345.06655.14055.21545.29135.36805.44575.52425.60385.68425.76565.84805.93136.01566.10086.187055.10105.20405.30915.41635.52565.63715.75075.86665.98476.10516.22786.35286.48036.61016.74246.87717.01447.15427.29667.44167.58927.73967.89268.04848.20708.36848.53278.69998.87009.0431
66.15206.30816.46846.63306.80196.97537.15337.33597.52337.71567.91298.11528.32278.53558.75378.97759.20689.44209.68309.929910.183010.442310.707910.980111.258811.544211.836612.135912.442312.756077.21357.43437.66257.89838.14208.39388.65408.92289.20049.48729.783310.089010.404710.730511.066811.413911.772012.141512.522712.915913.321413.739614.170814.615315.073515.545816.032416.533917.050617.582888.28578.58308.89239.21429.54919.897510.259810.636611.028511.435911.859412.299712.757313.232813.726814.240114.773315.327015.902016.499117.118917.762318.430019.122919.841920.587621.361222.163422.995323.857799.36859.754610.159110.582811.026611.491311.978012.487613.021013.579514.164014.775715.415716.085316.785817.518518.284719.085919.923420.798921.713922.670023.669024.712525.802326.940428.128729.369230.663932.01501010.462210.949711.463912.006112.577913.180813.816414.486615.192915.937416.722017.548718.419719.337320.303721.321522.393123.521324.708925.958727.273828.657430.112831.643433.252934.944936.723538.592640.556442.6195
1111.566812.168712.807813.486414.206814.971615.783616.645517.560318.531219.561420.654621.814323.044524.349325.732927.199928.755130.403532.150434.001335.962038.038840.237942.566145.030647.638850.398553.317856.40531212.682513.412114.192015.025815.917116.869917.888518.977120.140721.384322.713224.133125.650227.270729.001730.850232.823934.931137.180239.580542.141644.873747.787750.895054.207757.738661.501365.510069.780074.32701313.809314.680315.617816.626817.713018.882120.140621.495322.953424.522726.211628.029129.984732.088734.351936.786239.404042.218745.244548.496651.991355.745959.778864.109768.759673.750679.106684.852991.016197.62501414.947415.973917.086318.291919.598621.015122.550524.214926.019227.975030.094932.392634.882737.581140.504743.672047.102750.818054.840959.195963.909569.010074.528080.496186.949593.9258101.4654109.6117118.4108127.91251516.096917.293418.598920.023621.578623.276025.129027.152129.360931.772534.405437.279740.417543.842447.580451.659556.110160.965366.260772.035178.330585.192292.6694100.8151109.6868119.3465129.8611141.3029153.7500167.2863
1617.257918.639320.156921.824523.657525.672527.888130.324333.003435.949739.189942.753346.671750.980455.717560.925066.648872.939079.850287.442195.7799104.9345114.9834126.0108138.1085151.3766165.9236181.8677199.3374218.47221718.430420.012121.761623.697525.840428.212930.840233.750236.973740.544744.500848.883753.739159.117665.075171.673078.979287.068096.0218105.9306116.8937129.0201142.4295157.2534173.6357191.7345211.7230233.7907258.1453285.01391819.614721.412323.414425.645428.132430.905733.999037.450241.301345.599250.395955.749761.725168.394175.836484.140793.4056103.7403115.2659128.1167142.4413158.4045176.1883195.9942218.0446242.5855269.8882300.2521334.0074371.51801920.810922.840625.116927.671230.539033.760037.379041.446346.018551.159156.939563.439770.749478.969288.211898.6032110.2846123.4135138.1664154.7400173.3540194.2535217.7116244.0328273.5558306.6577343.7580385.3227431.8696483.97342022.019024.297426.870429.778133.066036.785640.995545.762051.160157.275064.202872.052480.946891.0249102.4436115.3797130.0329146.6280165.4180186.6880210.7584237.9893268.7853303.6006342.9447387.3887437.5726494.2131558.1118630.1655
2123.239225.783328.676531.969235.719339.992744.865250.422956.764564.002572.265181.698792.4699104.7684118.8101134.8405153.1385174.0210197.8474225.0256256.0176291.3469331.6059377.4648429.6809489.1098556.7173633.5927720.9642820.21512224.471627.299030.536834.248038.505243.392349.005755.456862.873371.402781.214392.5026105.4910120.4360137.6316157.4150180.1721206.3448236.4385271.0307310.7813356.4432408.8753469.0563538.1011617.2783708.0309811.9987931.04381067.27962325.716328.845032.452936.617941.430546.995853.436160.893369.531979.543091.1479104.6029120.2048138.2970159.2764183.6014211.8013244.4868282.3618326.2369377.0454435.8607503.9166582.6298673.6264778.7707900.19931040.35831202.04651388.46352426.973530.421934.426539.082644.502050.815658.176766.764876.789888.4973102.1742118.1552136.8315158.6586184.1678213.9776248.8076289.4945337.0105392.4842457.2249532.7501620.8174723.4610843.0329982.25111144.25311332.65861551.64001806.00262528.243232.030336.459341.645947.727154.864563.249073.105984.700998.3471114.4133133.3339155.6196181.8708212.7930249.2140292.1049342.6035402.0425471.9811554.2422650.9551764.6054898.09161054.79121238.63631454.20141706.80312002.61562348.8033
2629.525633.670938.553044.311751.113559.156468.676579.954493.3240109.1818127.9988150.3339176.8501208.3327245.7120290.0883342.7627405.2721479.4306567.3773671.6330795.1653941.46471114.63361319.48901561.68181847.83582185.70792584.37413054.44432730.820935.344340.709647.084254.669163.705874.483887.3508102.7231121.0999143.0786169.3740200.8406238.4993283.5688337.5024402.0323479.2211571.5224681.8528813.6759971.10161159.00161383.14571650.36121968.71912347.75152798.70613334.84263971.77762832.129137.051242.930949.967658.402668.528180.697795.3388112.9682134.2099159.8173190.6989227.9499272.8892327.1041392.5028471.3778566.4809681.1116819.2233985.54791185.74401426.57191716.10072063.95152481.58602982.64443583.34384302.94705164.31092933.450438.792245.218952.966362.322773.639887.3465103.9659124.1354148.6309178.3972214.5828258.5834312.0937377.1697456.3032552.5121669.4475811.5228984.06801193.51291447.60771755.68352128.96482580.93943127.79843788.95834587.68015551.80166714.60423034.784940.568147.575456.084966.438879.058294.4608113.2832136.3075164.4940199.0209241.3327293.1992356.7868434.7451530.3117647.4391790.9480966.71221181.88161445.15071767.08132160.49072640.91643227.17433942.02604812.97715873.23067162.82418729.9855