年金终值系数-详解.docx

年金终值系数-详解 目录 1 什么是年金终值系数 2 年金终值系数公式的推导 3 年金终值系数的应用实例 4 年金终值系数表 5 相关条目什么是年金终值系数　　年金终值系数指固定的间隔时间相等的期间(如以年为单位)分期支付(存入)1元金额，经过若干年后按复利计算的累计本利之和　　年金终值系数公式如下：　　年金终值系数（Future value of an annuity factor）=F/A=(F/A,i,n)　　　　这里F/A=(F/A,i,n)代表年金终值系数，i代表利率，n代表年数年金终值系数公式的推导　　该公式可由复利公式推导出来，推导过程如下：　　第1年存入1元到第n年的本利和 = (1 + i)n − 1　　第2年存入1元到第n年的本利和 = (1 + i)n − 2　　......　　第(n-1)年存入1元到第n年的本利和=(1+i)　　第n年存入l元 = (1 + i)0　　因此，各年本利和相加得：　　An | i = (1 + i)n − 1 + (1 + i)n − 2...... + (1 + i) + 1　　　(1)　　两边乘以(1+i)，则　　(1 + i)An | i = (1 + i)n + (1 + i)n − 1 + ...... + (1 + i)　　　(2)　　(2)-(1)得iAn | i = (1 + i)n − 1，即　　年金终值系数的应用实例　　例：按年利率10％计算5年的年金终值系数如下：　　　　为了方便年金终值系数的运用，对不同年数不同利率分别计算出年金终值系数，列示成年金终值系数表。

亦称“1元普通年金终值表”运用年金终值系数求等额支付若干年后的年金终值就很方便例：每年存入银行100元，按年利率l0%复利计算，第5年后的本利和(用A表示)为多少?计算如 下：　　(1)用公式计算　　　　 元　　(2)查表计算　　 元年金终值系数表期数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%11.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000022.01002.02002.03002.04002.05002.06002.07002.08002.09002.10002.11002.12002.13002.14002.15002.16002.17002.18002.19002.20002.21002.22002.23002.24002.25002.26002.27002.28002.29002.300033.03013.06043.09093.12163.15253.18363.21493.24643.27813.31003.34213.37443.40693.43963.47253.50563.53893.57243.60613.64003.67413.70843.74293.77763.81253.84763.88293.91843.95413.990044.06044.12164.18364.24654.31014.37464.43994.50614.57314.64104.70974.77934.84984.92114.99345.06655.14055.21545.29135.36805.44575.52425.60385.68425.76565.84805.93136.01566.10086.187055.10105.20405.30915.41635.52565.63715.75075.86665.98476.10516.22786.35286.48036.61016.74246.87717.01447.15427.29667.44167.58927.73967.89268.04848.20708.36848.53278.69998.87009.043166.15206.30816.46846.63306.80196.97537.15337.33597.52337.71567.91298.11528.32278.53558.75378.97759.20689.44209.68309.929910.183010.442310.707910.980111.258811.544211.836612.135912.442312.756077.21357.43437.66257.89838.14208.39388.65408.92289.20049.48729.783310.089010.404710.730511.066811.413911.772012.141512.522712.915913.321413.739614.170814.615315.073515.545816.032416.533917.050617.582888.28578.58308.89239.21429.54919.897510.259810.636611.028511.435911.859412.299712.757313.232813.726814.240114.773315.327015.902016.499117.118917.762318.430019.122919.841920.587621.361222.163422.995323.857799.36859.754610.159110.582811.026611.491311.978012.487613.021013.579514.164014.775715.415716.085316.785817.518518.284719.085919.923420.798921.713922.670023.669024.712525.802326.940428.128729.369230.663932.01501010.462210.949711.463912.006112.577913.180813.816414.486615.192915.937416.722017.548718.419719.337320.303721.321522.393123.521324.708925.958727.273828.657430.112831.643433.252934.944936.723538.592640.556442.61951111.566812.168712.807813.486414.206814.971615.783616.645517.560318.531219.561420.654621.814323.044524.349325.732927.199928.755130.403532.150434.001335.962038.038840.237942.566145.030647.638850.398553.317856.40531212.682513.412114.192015.025815.917116.869917.888518.977120.140721.384322.713224.133125.650227.270729.001730.850232.823934.931137.180239.580542.141644.873747.787750.895054.207757.738661.501365.510069.780074.32701313.809314.680315.617816.626817.713018.882120.140621.495322.953424.522726.211628.029129.984732.088734.351936.786239.404042.218745.244548.496651.991355.745959.778864.109768.759673.750679.106684.852991.016197.62501414.947415.973917.086318.291919.598621.015122.550524.214926.019227.975030.094932.392634.882737.581140.504743.672047.102750.818054.840959.195963.909569.010074.528080.496186.949593.9258101.4654109.6117118.4108127.91251516.096917.293418.598920.023621.578623.276025.129027.152129.360931.772534.405437.279740.417543.842447.580451.659556.110160.965366.260772.035178.330585.192292.6694100.8151109.6868119.3465129.8611141.3029。