什么是“复利终值”.docx

专业、可靠的创新型互联网金融平台什么是“复利终值”复利是计算利息的一种方法。按照这种方法，每经过一个计息期，要将所生利息加入本金再计利息，逐期滚算，俗称“利滚利”。这里所说的计息期是指相邻两次计息的时间间隔，如年、月、日等。除非特别指明，计息期为1年。所谓复利，实际上就是我们通常所说的利滚利。即每经过一个计息期，要将利息加入本金再计利息，逐期计算。终值是指最后得到的数据。因此，复利终值就是指一笔收支经过若干期后再到期时的金额，这个金额和最初的收支额事实上具有相同的支付能力。中文名复利终值外文名复利终值所谓复利方法计算利息要了解复利终值，必须先了解单利单利是在任一个计息期均仅按照初始资本计算利息，而不计算到期利息的利息的一种计息方式。银行存款多用这种计息方式。公式为：相对的，复利是在任一个计息期均按照本息和计算利息，而仅不计算初始资金的利息的一种计息方式。银行贷款多用这种计息方式。公式为：上述是计算复利终值的一般公式，其中的被称为复利终值系数或1元的复利终值，用符号（S/P,i,n）表示。例如，（S/P,6%,3）表示利率为6%的3期复利终值的系数。为了便于计算，可编制“复利终值系数表”备用。该表的第一行是利率i，第一列是计息期数n，相应的值在其纵横相交处。通过该表可以查出，（S/P,6%,3）=1.1910（保留四位小数的近似值）。在时间价值为6%的情况下，存入时的1元和3年后的1.1910元在经济上是等效的，根据这个系数可以把现值换算成终值。公式公式推导：根据复利的概念，计算某一笔钱的终值，可用以下公式计算：但是由于这样计算的话，如果期限太长的话，这个累加计算是非常麻烦的，因此，我们通常把公式简化、因式分解为：而其中提取掉x后的幂指数称为复利终值系数。示例实例一例：张三拟投资10万元于一项目，该项目的投资期为5年，每年的投资报酬率为20%，张三盘算着：这10万元本金投入此项目后，5年后可以收回的本息合计为多少？分析：由于货币随时间的增长过程与复利的计算过程在数学上是相似的，因此，在计算货币的时间价值时，可以使用复利计算的各种方法。张三的这笔账实际上是关于复利终值的计算问题。假如张三在期初投入资金100000元，利息用i表示，那么：经过1年的时间后，张三的本利和（元）经过2年的时间后，张三的本利和（元）依次类推，5年后，张三的本利和（元）我们称（1+i）n为复利终值系数，在实际运用时，通常查表得到其解。查复利终值表，得知当i=20%，n=5时，复利终值系数为2.4883，那么5年后张三的本利和=1000002.4883=248830元。当然，之所以系数表中的系数使用时与直接的幂指数计算结果有微小的差异，那是因为系数表中的系数不可能每一个系数精确到它的最后一位小数位，而是保留至多4位小数。S为复利终值 P为复利现值 i为年收益率或利率 n为投资期限实例二例如，某人将10000元投资于一项事业，年报酬率为6%。按单利计算：经过1年时间的期终金额为：=10600（元）其中：P现值或初始值；i报酬率或利率；S终值或本利和。若此人不提走现金，则第2年本利和为：=11200(元)同理，第3年的期终金额为：=11800(元)仍以上例为例，按复利计算：经过1年时间的期终金额为：=10600（元）若此人不提走现金，则第2年本利和为：=11236（元）同理，第3年的期终金额为：=11910.16（元）C语言计算#include stdio.h#include void main()float p,s,x,z,n;float i;printf(输入现金回车输入收益率回车输入投资年限回车n);scanf(%f%f%f,&p,&i,&x);/您投资了多少现金%d,您的年收益率是多少%d,您的投资了多少年n=1+i;z=(float)(pow(n,x);s=p*z;printf(您的现金终值为%f,s);2复利终值系数表编辑本词条提供1%50%利率150期的复利终值系数（精确到万分位）供查询。但因利率越高、期数越长，会导致数据过长，所以本表特意每5个百分点分出一张表格，合计10张表格，以免系数出现表内换行的情形。表一（1%5%利率）复利终值系数表利息期数1%2%3%4%5%11.01001.02001.03001.04001.050021.02011.04041.06091.08161.102531.03031.06121.09271.12491.157641.04061.08241.12551.16991.215551.05101.10411.15271.21671.276361.06151.12621.19411.26531.340171.07211.14871.22991.31591.407181.08291.17171.26681.36861.477591.09371.19511.30481.42331.5513101.10461.21901.34391.48021.6289111.11571.24341.38421.53951.7103121.12681.26841.42581.60101.7959131.13811.29361.46851.66511.8856141.14951.31951.51261.73171.9799151.16101.34591.55801.80092.0789161.17261.37281.60471.87302.1829171.18433.40021.65281.94792.2920181.19611.42821.70242.02582.4066191.20811.45681.75352.10682.5270201.22021.48591.80612.19112.6533211.23241.51571.86032.27882.7860221.24471.54601.91612.36992.9253231.25721.57691.97352.46473.0715241.26971.60842.03282.56333.2251251.28241.64062.09382.66583.3864261.29531.67342.15662.77253.5557271.30821.70692.22132.88343.7335281.32131.74102.28792.99873.9201291.33451.77582.35663.11874.1161301.34781.81142.42733.24344.3219311.36131.84762.50013.37314.5380321.37491.88452.57513.50814.7649331.38871.92222.65233.64845.0032341.40261.96072.73193.79435.2533351.41661.99992.81393.94615.5160361.43082.03992.89834.10395.7918371.44512.08072.98524.26816.0814381.45952.12233.07484.43886.3855391.47412.16473.16704.61646.7048401.48892.20803.26204.80107.0400411.50382.25223.35994.99317.3920421.51882.29723.46075.19287.7616431.53402.34323.56455.40058.1500441.54932.39013.67155.61658.5572451.56482.43793.78165.84128.9850461.58052.48663.89506.07489.4343471.59632.53634.01196.31789.9060481.61222.58714.13236.570510.4013491.62832.63884.25626.833310.9213501.64462.69164.38397.106711.46743表二（6%10%利率）复利终值系数表（续表一）利率期数6%7%8%9%10%11.06001.07001.08001.09001.100021.12361.14491.16641.18811.210031.19101.22501.25971.29501.331041.26251.31081.36051.41161.464151.33821.40261.46931.53861.610561.41851.50071.58691.67711.771671.50361.60581.71381.82801.948781.59381.71821.85091.99262.143691.68951.83851.99902.17192.3579101.79081.96722.15892.36742.5937111.89832.10492.33162.58042.8531122.01222.25222.51822.81273.1384132.13292.40982.71963.06583.4522142.26092.57852.93723.34173.7975152.39662.75903.17223.64254.1772162.54042.95223.42593.97034.5950172.69283.15883.70004.32765.0545182.85433.37993.99604.71715.5599193.02563.61654.31575.14176.1159203.20713.86974.66105.60446.7275213.39964.14065.03386.10887.4002223.60354.43045.43656.65868.1403233.81984.74055.87157.25798.9543244.04895.07246.34127.91119.8497254.29195.42746.84858.623110.8347264.54945.80747.39649.399211.9182274.82236.21397.988110.245113.1100285.11176.64888.627111.167114.4210295.41847.11439.317312.172215.8631305.74357.612310.062713.267717.4494316.08818.145110.867714.461819.1943326.45348.715311.737115.763321.1138336.84069.325312.676017.182023.2252347.25109.978113.690118.728425.5477357.686110.676614.785320.414028.1024368.147311.423915.968222.251230.9127378.636112.223617.245624.253834.0039389.154313.079318.625326.436737.4043399.703513.994820.115328.816041.14484010.285714.974521.724531.409445.25934110.902916.022723.462534.236349.78524211.557017.144325.339537.317554.76374312.250518.344427.366640.676160.24014412.985519.628529.556044.337066.26414513.764621.002531.920448.327372.89054614.590522.472634.474152.676780.17954715.465924.045737.232057.417688.19754816.393925.728940.210662.585297.01724917.377527.529943.427468.2179106.71905018.420229.457046.901674.3575117.39094表三（11%15%利率）复利终值系数表（续表二）利率期数11%12%13%14%15%11.11001.12001.13001.14001.150021.23211.25441.27691.29961.322531.36761.40491.44291.48151.520941.51811.57351.63051.68901.749051.68511.76231.84241.92542.011461.87041.97382.08202.19502.313172.07622.21072.35262.50232.660082.30452.47602.65842.85263.059092.55802.77313.00403.25193.5179102.83943.10583.39463.70724.0456113.15183.47853.83594.22624.6524123.49853.89604.33454.81795.3503133.88334.36354.89805.49246.1528144.31044.88715.53486.26137.0757154.78465.47366.25437.13798.1371165.31096.13047.06738.13729.3576175.89516.86607.98619.276510.7613186.54367.69009.024310.575212.3755197.26338.612810.197412.055714.2318208.06239.646311.523113.743516.3665218.949210.803813.021115.667618.8215229.933612.100314.713817.861021.64472311.026313.552316.626620.361624.89152412.239215.178618.788123.212228.62522513.585517.000121.230526.461932.91902615.079919.040123.990530.166637.85682716.738621.324927.109334.389943.53532818.579923.883930.633539.204550.06562920.623726.749934.615844.693157.57553022.892329.959939.115950.950266.21183125.410433.555144.201058.083276.14353228.205637.581749.947166.214887.56513331.308242.091556.440275.4849100.69983434.752147.142563.777486.0528115.80483538.574952.799672.068598.1002133.17553642.818159.135681.4374111.8342153.15193747.528166.231892.0243127.4910176.12463852.756274.1797103.9874145.3397202.54333958.559383.0812117.5058165.6873232.92484065.000993.0510132.7816188.8835267.86354172.1510104.2171150.0432215.3272308.04314280.0876116.2314169.5488245.4730354.24954388.8972130.7299191.5901279.8392407.38704498.6759146.4175216.4968319.0167468.495045109.5302163.9876244.6414363.6791538.769346121.5786183.6661276.4448414.5941619.584747134.9522205.7061312.3826472.6373712.522448149.7970230.3908352.9923538.8065819.400749166.2746258.0377398.8813614.2395942.310850184.5648289.0022450.7359700.23301,083.65745表四（16%20%利率）复利终值系数表（续表三）利率期数16%17%18%19%20%11.16001.17001.18001.19001.200021.34561.36891.39241.41611.440031.56091.60161.64301.68521.728041.81061.87391.93882.00532.073652.10032.19242.28782.38642.488362.43642.56522.69962.83982.986072.82623.00123.18553.37933.583283.27843.51153.75894.02144.299893.80304.10844.43554.78545.1598104.41144.80685.23385.69476.1917115.11735.62406.17596.77677.4301125.93606.58017.28768.06428.9161136.88587.69878.59949.596410.6993147.98759.007510.147211.419812.8392159.265510.538711.973713.589515.40701610.748012.330314.129016.171518.48841712.467714.426516.672219.244122.18611814.462516.879019.673322.900526.62331916.776519.748423.214427.251631.94802019.460823.105627.393032.429438.33762122.574527.033632.323838.591046.00512226.186431.629338.142145.923355.20612330.376237.006245.007654.648766.24742435.236443.297353.109065.032079.49682540.874250.657862.668677.388195.39622647.414159.269773.949092.0918114.47552755.000469.345587.2598109.5893137.37062863.800481.1342102.9666130.4112164.84472974.008594.9271121.5005155.1893197.81363085.8499111.0647143.3706184.6753237.37633199.5859129.9456169.1774219.7636284.851632115.5196152.0364199.6293261.5187341.821933134.0027177.8826235.5625311.2073410.186334155.4432208.1226277.9638370.3366492.223535180.3141243.5035327.9973440.7006590.668236209.1643284.8991387.0368524.4337708.801937242.6306333.3319456.7034624.0761850.562338281.4515389.9983538.9100742.65061,020.674739326.4838456.2980635.9139883.75421,224.809640378.7212533.8687750.37831,051.66751,469.771641439.3165624.6264885.44641,251.48431,763.725942509.6072730.81291,044.82681,489.26642,116.471143591.1443855.05111,232.89561,772.22702,539.765344685.72741,000.40981,454.81682,108.95013,047.718345795.44381,170.47941,716.68392,509.65063,657.262046922.71481,369.46092,025.68702,986.48424,388.7144471,070.34921,602.26922,390.31063,553.91625,266.4573481,241.60511,874.65502,820.56654,229.16036,319.7487491,440.26192,193.34643,328.26855,032.70087,583.6985501,670.70382,566.21533,927.35695,988.91399,100.41825表五（21%25%利率）复利终值系数表（续表四）利率期数21%22%23%24%25%11.21001.22001.23001.24001.250021.46411.48841.51291.53761.562531.77161.81581.86091.90661.953142.14362.21532.28892.36422.441452.59372.70272.81532.93163.051863.13843.29733.46283.63523.814773.79754.02274.25934.50774.768484.59504.90775.23895.58955.960595.55995.98746.44396.93107.4506106.72757.30467.92598.59449.3132118.14038.91179.748910.657111.6415129.849710.872211.991213.214814.55191311.918213.264114.749116.386318.18991414.421016.182218.141420.319122.73741517.449419.742322.314025.195628.42171621.113824.085627.446231.242635.52711725.547729.384433.758838.740844.40891830.912735.849041.523348.038655.51121937.404343.735851.073759.567969.38892045.259353.357662.820673.864186.73622154.763765.096377.269491.5915108.42022266.264179.417595.0413113.5735135.52532380.179596.8893116.9008140.8312169.40662497.0172118.2050143.7880174.6306211.758225117.3909144.2101176.8593216.5420264.697826142.0429175.9364217.5369268.5121330.872227171.8719214.6424267.5704332.9550413.590328207.9651261.8637329.1115412.8642516.987929251.6377319.4737404.8072511.9516646.234930304.4816389.7579497.9129634.8199807.793631368.4228475.5046612.4328787.17671,009.742032445.7916580.1156753.2924976.09911,262.177433539.4078707.7411926.54961,210.36291,577.721834652.6834863.44411,139.65601,500.85001,972.152335789.74701,053.40181,401.77691,861.05402,465.190336955.59381,285.15021,724.18562,307.70703,081.4879371,156.26851,567.88332,120.74832,861.55673,851.8599381,399.08491,912.81762,608.52043,548.33034,814.8249391,692.89272,333.63753,208.48014,399.92956,018.5311402,048.40022,847.03783,946.43055,455.91267,523.1638412,478.56433,473.38614,854.10956,765.33179,403.9548422,999.06284,237.53105,970.55478,389.011311,754.9435433,628.86595,169.78787,343.782310,402.374014,693.6794444,390.92786,307.14119,032.852212,898.943718,367.0992455,313.02267,694.712211,110.408215,994.690222,958.8740466,428.75749,387.548913,665.802119,833.415828,698.5926477,778.796411,452.809616,808.936524,593.435635,873.2407489,412.343713,972.427720,674.992030,495.860244,841.55094911,388.935817,046.361925,430.240137,814.866656,051.93865013,780.612320,796.561531,279.195346,890.434670,064.92326表六（26%30%利率）复利终值系数表（续表五）利率期数26%27%28%29%30%11.26001.27001.28001.29001.300021.58761.61291.68341.66411.690032.00042.04842.09722.14672.197042.52052.60142.68442.76922.856153.17583.30383.43603.57233.712964.00154.19594.39804.60834.826875.04195.32885.62955.94476.274986.35286.76757.20587.66868.157398.00458.59479.22349.892510.60451010.085710.915311.805912.761413.78581112.708013.862515.111616.462217.92161216.012017.605319.342821.236223.29811320.175222.358824.758827.394730.28751425.420728.395731.691335.339139.37381532.030136.062540.564845.587551.18591640.357945.799451.923058.807966.54171750.851058.165266.461475.862186.50421864.072273.869885.070697.8622112.45541980.731093.8147108.8904126.2422146.192020101.7211119.1446139.3797162.8524190.049621128.1685151.3137178.4060210.0796247.064522161.4624192.1683228.3596271.0027321.183923203.4804244.0538292.3003349.5935417.539124256.3853309.0483374.1444450.9756542.800825323.0454393.6344478.9049581.7585705.641026407.0373499.9157612.9982750.4685917.333327512.8670634.8929784.6377968.10441,192.533328646.2124806.31401,004.33631,248.85461,550.293329814.22761,024.01871,285.55041,611.02252,015.3813301,025.92671,300.50381,645.50462,078.21902,619.9956311,292.66771,651.63982,106.24582,680.90253,405.9943321,628.76132,097.58262,695.99473,458.36424,427.7926332,052.23922,663.92993,450.87324,461.28985,756.1304342,585.82153,383.19104,417.11775,755.06397,482.9696353,258.13504,296.65255,653.91067,424.03249,727.8604364,105.25015,456.74877,237.00569,577.001812,646.2186375,172.61526,930.07099,263.367112,354.332416,440.0841386,517.49518,801.190011,857.109915,937.088821,372.1094398,212.043811,177.511315,177.100720,558.844527,783.74224010,347.175314,195.439319,426.688926,520.909436,118.86484113,037.440818,028.208024,866.161834,211.973146,954.52434216,427.175422,895.824131,828.687144,133.445361,040.88154320,698.241029,077.696640,740.719556,932.144579,353.14604426,079.783736928.674752,148.121073,442.4664103,159.08984532,860.527546,899.416966,749.594994,740.7816134,106.81674641,404.264659,562.259485,439.4814122,215.6083174,338.86174752,169.373475,644.0695109,362.5362157,658.1347226,640.52024865,733.410596,067.9683139,984.0464203,378.9938294,632.67634982,824.0972122,006.3197179,179.5794262,358.9020383,022.479250104,358.3625154,948.0260229,349.8616338,442.9836497,929.22307表七（31%35%利率）复利终值系数表（续表六）利率期数31%32%33%34%35%11.31001.32001.33001.34001.350021.71611.74241.76891.79561.822532.24812.29992.35262.40612.460442.94503.03603.12903