一、年金終值係數指固定的間隔時間相等的期間(如以年為單位)分期支付(存入)1元金額,經過若干年後按複利計算的累計本利之和。
年金終值係數公式如下: ,這裡F/A=(F/A,i,n)代表年金終值係數,i代表 利率,n代表年數。
二、 在Excel中我們可以使用FV財務函數計算年金終值係數,我們先來學習一下FV函數。FV 是一個財務函數,用於根據固定利率計算投資的未來值。可以將 FV 與定期付款、固定付款或一次付清總額付款結合使用。
1.FV函數語法
FV(rate,nper,pmt,[pv],[type])
FV 函數有下列參數:
Rate 必需。各期利率。
Nper 必需。年金的付款總期數。
Pmt 必需。各期所應支付的金額,在整個年金期間保持不變。通常 pmt 包括本金和利息,但不包括其他費用或稅款。如果省略 pmt,則必須包括 pv 參數。
pv 可選。現值,或一系列未來付款的當前值的累積和。如果省略 pv,則假定其值為 0(零),並且必須包括 pmt 參數。
Type 可選。數字 0 或 1,用以指定各期的付款時間是在期初還是期末。如果省略 type,則假定其值為 0。
2. 假如我們計算3年期5%利率的年金終值係數,公式為FV(5%,3,-1, ,0),這裡-1表示收到的金額,如下圖所示。
圖1.Excel函數FV計算年金終值係數。
附年金終值係數表
利率1%2%3%4%5%6%7%8%9%10%期數
11.00001.00001.00001.00001.00001.00001.00001.00001.00001.000022.01002.02002.03002.04002.05002.06002.07002.08002.09002.100033.03013.06043.09093.12163.15253.18363.21493.24643.27813.310044.06044.12164.18364.24654.31014.37464.43994.50614.57314.641055.10105.20405.30915.41635.52565.63715.75075.86665.98476.105166.15206.30816.46846.63306.80196.97537.15337.33597.52337.715677.21357.43437.66257.89838.14208.39388.65408.92289.20049.487288.28578.58308.89239.21429.54919.897510.259810.636611.028511.435999.36859.754610.159110.582811.026611.491311.978012.487613.021013.57951010.462210.949711.463912.006112.577913.180813.816414.486615.192915.93741111.566812.168712.807813.486414.206814.971615.783616.645517.560318.53121212.682513.412114.192015.025815.917116.869917.888518.977120.140721.38431313.809314.680315.617816.626817.713018.882120.140621.495322.953424.52271414.947415.973917.086318.291919.598621.015122.550524.214926.019227.97501516.096917.293418.598920.023621.578623.276025.129027.152129.360931.77251617.257918.639320.156921.824523.657525.672527.888130.324333.003435.94971718.430420.012121.761623.697525.840428.212930.840233.750236.973740.54471819.614721.412323.414425.645428.132430.905733.999037.450241.301345.59921920.810922.840625.116927.671230.539033.760037.379041.446346.018551.15912022.019024.297426.870429.778133.066036.785640.995545.762051.160157.27502123.239225.783328.676531.969235.719339.992744.865250.422956.764564.00252224.471627.299030.536834.248038.505243.392349.005755.456862.873371.40272325.716328.845032.452936.617941.430546.995853.436160.893369.531979.54302426.973530.421934.426539.082644.502050.815658.176766.764876.789888.49732528.243232.030336.459341.645947.727154.864563.249073.105984.700998.34712629.525633.670938.553044.311751.113559.156468.676579.954493.3240109.18182730.820935.344340.709647.084254.669163.705874.483887.3508102.7231121.09992832.129137.051242.930949.967658.402668.528180.697795.3388112.9682134.20992933.450438.792245.218952.966362.322773.639887.3465103.9659124.1354148.63093034.784940.568147.575456.084966.438879.058294.4608113.2832136.3075164.49403136.132742.379450.002759.328370.760884.8017102.0730123.3459149.5752181.94343237.494144.227052.502862.701575.298890.8898110.2182134.2135164.0370201.13783338.869046.111655.077866.209580.063897.3432118.9334145.9506179.8003222.25153440.257748.033857.730269.857985.0670104.1838128.2588158.6267196.9823245.47673541.660349.994560.462173.652290.3203111.4348138.2369172.3168215.7108271.02443643.076951.994463.275977.598395.8363119.1209148.9135187.1021236.1247299.12683744.507654.034366.174281.7022101.6281127.2681160.3374203.0703258.3759330.03953845.952756.114969.159485.9703107.7095135.9042172.5610220.3159282.6298364.04343947.412358.237272.234290.4091114.0950145.0585185.6403238.9412309.0665401.44784048.886460.402075.401395.0255120.7998154.7620199.6351259.0565337.8824442.59264150.375262.610078.663399.8265127.8398165.0477214.6096280.7810369.2919487.85184251.879064.862282.0232104.8196135.2318175.9505230.6322304.2435403.5281537.63704353.397867.159585.4839110.0124142.9933187.5076247.7765329.5830440.8457592.40074454.931869.502789.0484115.4129151.1430199.7580266.1209356.9496481.5218652.64084556.481171.892792.7199121.0294159.7002212.7435285.7493386.5056525.8587718.90484658.045974.330696.5015126.8706168.6852226.5081306.7518418.4261574.1860791.79534759.626376.8172100.3965132.9454178.1194241.0986329.2244452.9002626.8628871.97494861.222679.3535104.4084139.2632188.0254256.5645353.2701490.1322684.2804960.17234962.834881.9406108.5406145.8337198.4267272.9584378.9990530.3427746.86561057.18965064.463284.5794112.7969152.6671209.3480290.3359406.5289573.7702815.08361163.9085