單利、復(fù)利和年金的計算(有附表)

1、精選優(yōu)質(zhì)文檔-傾情為你奉上單利、復(fù)利和年金的計算（有附表）一、單利的終值和現(xiàn)值設(shè)定I為利息；P為現(xiàn)值；F為終值；i為每一利息期的利率（折現(xiàn)率）；n為計算利息的期數(shù)。復(fù)利計算的符號標(biāo)識相同。按照單利的計算法則，利息的計算公式為在計算利息時，除非特別指明，一般給出的利率均為年利率，對于不足一年的利息，以一年等于360天來折算。單利終值的計算公式如下：單利現(xiàn)值的計算與單利終值的計算是互逆的，由終值計算現(xiàn)值的過程稱為折現(xiàn)。單利現(xiàn)值的計算公式為二、復(fù)利的終值和現(xiàn)值（一）復(fù)利終值（已知現(xiàn)值P，求終值F）資金時間價值通常是按復(fù)利計算的。復(fù)利不同于單利，它是“利上滾利”，既涉及本金上的利息，也涉及利上所生的利

2、息。復(fù)利終值是指一定量的本金按復(fù)利計算若干期后的本利和。其計算公式如下：計息期為二期以上時，復(fù)利的終值大于單利的終值，時間越長，相差越大。單利是隨時間的延長而按等差級數(shù)增長；復(fù)利則是按等比級數(shù)增長。在復(fù)利終值的計算公式中，表示本金為1元時，n期的復(fù)利終值，稱為1元的復(fù)利終值系數(shù)，也可寫成（F/P，i，n）。為了簡化運算，在計算復(fù)利終值時，可通過查“復(fù)利終值系數(shù)表”求得。（二）復(fù)利現(xiàn)值（已知終值F，求現(xiàn)值P）復(fù)利現(xiàn)值相當(dāng)于原始本金，它是指今后某一特定時間收到或付出的一筆款項，按折現(xiàn)率i所計算的現(xiàn)在時點價值。其計算公式為式中通常稱作1元的復(fù)利現(xiàn)值系數(shù)，記作(P/F，i，n)，可以直接查閱“復(fù)利現(xiàn)值

3、系數(shù)表”。上式也可寫作P=F(P/F，i，n)。三、年金（A）除了上述的一次性收付款項之外，在現(xiàn)實經(jīng)濟(jì)生活中，還存在一定時期內(nèi)每次等額收付的系列款項，即年金，通常用A表示。由于年金分為普通年金、即付年金、遞延年金、永續(xù)年金等幾種，有關(guān)終值和現(xiàn)值的計算方法不一樣，下面分別作介紹。（一）普通年金終值的計算（已知年金A，求年金終值F）普通年金是指從第一期起，在一定時期內(nèi)每期期末等額發(fā)生的系列收付款項，又稱后付年金。如果年金相當(dāng)于零存整取儲蓄存款的零存數(shù)，那么，年金終值就是零存整取的整取數(shù)，年金終值的計算公式為式中的分式稱作“年金終值系數(shù)”，記為(F/A, i, n)，可通過直接查

4、閱“年金終值系數(shù)表”求得有關(guān)數(shù)值。上式也可寫作。（二）年償債基金的計算（已知年金終值F，求年金A）償債基金是指為了在約定的未來某一時點清償某筆債務(wù)或積聚一定數(shù)額的資金而必須分次等額形成的存款準(zhǔn)備金。由于每次形成的等額準(zhǔn)備金類似年金存款，因而同樣可以獲得按復(fù)利計算的利息，所以債務(wù)實際上等于年金終值，每年提取的償債基金等于年金A。也就是說，償債基金的計算實際上是年金終值的逆運算。其計算公式為式中的分式稱作“償債基金系數(shù)”，記為(A/F, i, n)，可通過年金終值系數(shù)的倒數(shù)推算出來。上式也可寫作或（三）普通年金現(xiàn)值的計算（已知年金A，求年金現(xiàn)值P）年金現(xiàn)值是指一定時期內(nèi)每期期末

5、等額收付款項的復(fù)利現(xiàn)值之和。其現(xiàn)值的計算公式為式中的分式稱作“年金現(xiàn)值系數(shù)”，記為(P/A, i, n)，可通過直接查閱“年金現(xiàn)值系數(shù)表”求得有關(guān)數(shù)值。上式也可以寫作（四）年資本回收額的計算（已知年金現(xiàn)值P，求年金A）資本回收是指在給定的年限內(nèi)等額回收初始投入資本或清償所欠債務(wù)的價值指標(biāo)。年資本回收額的計算是年金現(xiàn)值的逆運算。其計算公式為式中的分式稱作“資本回收系數(shù)”，記為(A/P,i,n)，可利用年金現(xiàn)值系數(shù)的倒數(shù)求得。上式也可寫作，或（五）即付年金的終值與現(xiàn)值（已知年金A，求年金現(xiàn)值P）即付年金是指從第一期起，在一定時期內(nèi)每期期初等額收付的系列款項，也稱先付年金。它與普

6、通年金的區(qū)別僅在于付款時間的不同，前者發(fā)生在期初，后者發(fā)生在期末，兩者相差（1+i）。因此，即付年金的終值可用下列公式計算：即付年金現(xiàn)值的計算。如前所述，n期即付年金現(xiàn)值與n期普通年金現(xiàn)值的期限相同，但由于其付款時間不同，n期即付年金現(xiàn)值比n期普通年金現(xiàn)值少折現(xiàn)一期。因此，在n期普通年金現(xiàn)值的基礎(chǔ)上乘以(1+i)，便可求出n期即付年金的現(xiàn)值。其計算公式為（六）遞延年金現(xiàn)值的計算（已知年金A，求年金現(xiàn)值P）遞延年金是指第一次收付款發(fā)生時間與第一期無關(guān)，而是隔若干期（假設(shè)為m期，m1）后才開始發(fā)生的系列等額收付款項。它是普通年金的特殊形式，凡不是從第一期開始的年金都是遞延年金。遞延年金的現(xiàn)值可按以

7、下公式計算：（七）永續(xù)年金現(xiàn)值的計算永續(xù)年金是指無限期等額收付的特種年金，可視為普通年金的特殊形式，即期限趨于無窮的普通年金。存本取息可視為永續(xù)年金的例子。此外，也可將利率較高、持續(xù)期限較長的年金視同永續(xù)年金計算。由于永續(xù)年金持續(xù)期無限，沒有終止的時間，因此沒有終值，只有現(xiàn)值。通過普通年金現(xiàn)值計算可推導(dǎo)出永續(xù)年金現(xiàn)值的計算公式為附錄一：一元復(fù)利終值系數(shù)表 F=(1+i)n附錄二：一元復(fù)利現(xiàn)值系數(shù)表 P=(1+i)-n附錄三：一元年金終值系數(shù)表 F=(1+i)n-1/i附錄四：一元年金現(xiàn)值系數(shù)表 P=1-(1+i)-n/i專心-專注-專業(yè)附錄一：一元復(fù)利終值系數(shù)表 F=(1+i)nn1%2%3%

8、4%5%6%7%8%9%10%11%12%13%14%15%11.01001.02001.03001.04001.05001.06001.07001.08001.09001.10001.11001.12001.13001.14001.150021.02011.04041.06091.08161.10251.12361.14491.16641.18811.21001.23211.25441.27691.29961.322531.03031.06121.09271.12491.15761.19101.22501.25971.29501.33101.36761.40491.44291.48151.5

9、20941.04061.08241.12551.16991.21551.26251.31081.36051.41161.46411.51811.57351.63051.68901.749051.05101.10411.15931.21671.27631.33821.40261.46931.53861.61051.68511.76231.84241.92542.011461.06151.12621.19411.26531.34011.41851.50071.58691.67711.77161.87041.97382.08202.19502.313171.07211.14871.22991.315

10、91.40711.50361.60581.71381.82801.94872.07622.21072.35262.50232.660081.08291.17171.26681.36861.47751.59381.71821.85091.99262.14362.30452.47602.65842.85263.059091.09371.19511.30481.42331.55131.68951.83851.99902.17192.35792.55802.77313.00403.25193.5179101.10461.21901.34391.48021.62891.79081.96722.15892

11、.36742.59372.83943.10583.39463.70724.0456111.11571.24341.38421.53951.71031.89832.10492.33162.58042.85313.15183.47863.83594.22624.6524121.12681.26821.42581.60101.79592.01222.25222.51822.81273.13843.49853.89604.33454.81795.3503131.13811.29361.46851.66511.88562.13292.40982.71963.06583.45233.88334.36354

12、.89805.49246.1528141.14951.31951.51261.73171.97992.26092.57852.93723.34173.79754.31044.88715.53486.26137.0757151.16101.34591.55801.80092.07892.39662.75903.17223.64254.17724.78465.47366.25437.13798.1371161.17261.37281.60471.87302.18292.54042.95223.42593.97034.59505.31096.13047.06738.13729.3576171.184

13、31.40021.65281.94792.29202.69283.15883.70004.32765.05455.89516.86607.98619.276510.7613181.19611.42821.70242.02582.40662.85433.37993.99604.71715.55996.54367.69009.024310.575212.3755191.20811.45681.75352.10682.52703.02563.61654.31575.14176.11597.26338.612810.197412.055714.2318201.22021.48591.80612.191

14、12.65333.20713.86974.66105.60446.72758.06239.646311.523113.743516.3665211.23241.51571.86032.27882.78603.39964.14065.03386.10887.40028.949210.803813.021115.667618.8215221.24471.54601.91612.36992.92533.60354.43045.43656.65868.14039.933612.100314.713817.861021.6447231.25721.57691.97362.46473.07153.8197

15、4.74055.87157.25798.954311.026313.552316.626620.361624.8915241.26971.60842.03282.56333.22514.04895.07246.34127.91119.849712.239215.178618.788123.212228.6252251.28241.64062.09382.66583.38644.29195.42746.84858.623110.834713.585517.000121.230526.461932.9190301.34781.81142.42733.24344.32195.74357.612310

16、.062713.267717.449422.892329.959939.115950.950266.2118（續(xù)表）n16%17%18%19%20%21%22%23%24%25%26%27%28%29%30%11.16001.17001.18001.19001.20001.21001.22001.23001.24001.25001.26001.27001.28001.29001.300021.34561.36891.39241.41611.44001.46411.48841.51291.53761.56251.58761.61291.63841.66411.690031.56091.60161

17、.64301.68521.72801.77161.81581.86091.90661.95312.00042.04842.09722.14672.197041.81061.87391.93882.00532.07362.14362.21532.28892.36422.44142.52052.60142.68442.76922.856152.10032.19242.28782.38642.48832.59372.70272.81532.93163.05183.17583.30383.43603.57233.712962.43642.56522.69962.83982.98603.13843.29

18、733.46283.63523.81474.00154.19594.39804.60834.826872.82623.00123.18553.37933.58323.79754.02274.25934.50774.76845.04195.32885.62955.94476.274983.27843.51153.75894.02144.29984.59504.90775.23895.58955.96056.35286.76757.20587.66868.157393.80304.10844.43554.78545.15985.55995.98746.44396.93107.45068.00458

19、.59489.22349.892510.6045104.41144.80685.23385.69476.19176.72757.30467.92598.59449.313210.085710.915311.805912.761413.7858115.11735.62406.17596.77677.43018.14038.91179.748910.657111.641512.708013.862515.111616.462217.9216125.93606.58017.28768.06428.91619.849710.872211.991213.214814.551916.012017.6053

20、19.342821.236223.2981136.88587.69878.59949.596410.699311.918213.264114.749116.386318.189920.175222.358824.758827.394730.2875147.98759.007510.147211.419812.839214.421016.182218.141420.319122.737425.420728.395731.691335.339139.3738159.265510.538711.973713.589515.407017.449419.742322.314025.195628.4217

21、32.030136.062540.564845.587551.18591610.748012.330314.129016.171518.488421.113824.085627.446231.242635.527140.357945.799451.923058.807966.54171712.467714.426516.672219.244122.186125.547729.384433.758838.740844.408950.851058.165266.461475.862186.50421814.462516.879019.673322.900526.623330.912735.8490

22、41.523348.038655.511264.072273.869885.070697.8622112.45541916.776519.748423.214427.251631.948037.404343.735851.073759.567969.388980.731093.8147108.8904126.2422146.19202019.460823.105627.393032.429438.337645.259353.357662.820673.864186.7362101.7211119.1446139.3797162.8524190.04962122.574527.033632.32

23、3838.591046.005154.763765.096377.269491.5915108.4202128.1685151.3137178.4060210.0796247.06452226.186431.629338.142145.923355.206166.264179.417595.0413113.5735135.5253161.4924192.1683228.3596271.0027321.18392330.376237.006245.007654.648766.247480.179596.8894116.9008140.8312169.4066203.4804244.0538292

24、.3003349.5935417.53912435.236443.297353.109065.032079.496897.0172118.2050143.7880174.6306211.7582256.3853309.9483374.1444450.9756542.80082540.874250.657862.668677.388195.3962117.3909144.2101176.8593216.5420264.6978323.0454393.6344478.9049581.7585705.64103085.8499111.0647143.3706184.6753237.3763304.4

25、816389.7579497.9129634.8199807.79361025.92671300.50381645.50462078.21902619.9956附錄二：一元復(fù)利現(xiàn)值系數(shù)表 P=(1+i)-nn1%2%3%4%5%6%7%8%9%10%11%12%13%14%15%10.99010.98040.97090.96150.95240.94340.93460.92590.91740.90910.90090.89290.88500.87720.869620.98030.96120.94260.92460.90700.89000.87340.85730.84170.82640.81160.

26、79720.78310.76950.756130.97060.94230.91510.88900.86380.83960.81630.79380.77220.75130.73120.71180.69310.67500.657540.96100.92380.88850.85480.82270.79210.76290.73500.70840.68300.65870.63550.61330.59210.571850.95150.90570.86260.82190.78350.74730.71300.68060.64990.62090.59350.56740.54280.51940.497260.94

27、200.88800.83750.79030.74620.70500.66630.63020.59630.56450.53460.50660.48030.45560.432370.93270.87060.81310.75990.71070.66510.62270.58350.54700.51320.48170.45230.42510.39960.375980.92350.85350.78940.73070.67680.62740.58200.54030.50190.46650.43390.40390.37620.35060.326990.91430.83680.76640.70260.64460

28、.59190.54390.50020.46040.42410.39090.36060.33290.30750.2843100.90530.82030.74410.67560.61390.55840.50830.46320.42240.38550.35220.32200.29460.26970.2472110.89630.80430.72240.64960.58470.52680.47510.42890.38750.35050.31730.28750.26070.23660.2149120.88740.78850.70140.62460.55680.49700.44400.39710.35550

29、.31860.28580.25670.23070.20760.1869130.87870.77300.68100.60060.53030.46880.41500.36770.32620.28970.25750.22920.20420.18210.1625140.87000.75790.66110.57750.50510.44230.38780.34050.29920.26330.23200.20460.18070.15970.1413150.86130.74300.64190.55530.48100.41730.36240.31520.27450.23940.20900.18270.15990

30、.14010.1229160.85280.72840.62320.53390.45810.39360.33870.29190.25190.21760.18830.16310.14150.12290.1069170.84440.71420.60500.51340.43630.37140.31660.27030.23110.19780.16960.14560.12520.10780.0929180.83600.70020.58740.49360.41550.35030.29590.25020.21200.17990.15280.13000.11080.09460.0808190.82770.686

31、40.57030.47460.39570.33050.27650.23170.19450.16350.13770.11610.09810.08290.0703200.81950.67300.55370.45640.37690.31180.25840.21450.17840.14860.12400.10370.08680.07280.0611210.81140.65980.53750.43880.35890.29420.24150.19870.16370.13510.11170.09260.07680.06380.0531220.80340.64680.52190.42200.34180.277

32、50.22570.18390.15020.12280.10070.08260.06800.05600.0462230.79540.63420.50670.40570.32560.26180.21090.17030.13780.11170.09070.07380.06010.04910.0402240.78760.62170.49190.39010.31010.24700.19710.15770.12640.10150.08170.06590.05320.04310.0349250.77980.60950.47760.37510.29530.23300.18420.14600.11600.092

33、30.07360.05880.04710.03780.0304300.74190.55210.41200.30830.23140.17410.13140.09940.07540.05730.04370.03340.02560.01960.0151（續(xù)表）n16%17%18%19%20%21%22%23%24%25%26%27%28%29%30%10.86210.85470.84750.84030.83330.82640.81970.81300.80650.80000.79370.78740.78130.77520.769220.74320.73050.71820.70620.69440.683

34、00.67190.66100.65040.64000.62990.62000.61040.60090.591730.64070.62440.60860.59340.57870.56450.55070.53740.52450.51200.49990.48820.47680.46580.455240.55230.53370.51580.49870.48230.46650.45140.43690.42300.40960.39680.38440.37250.36110.350150.47610.45610.43710.41900.40190.38550.37000.35520.34110.32770.

35、31490.30270.29100.27990.269360.41040.38980.37040.35210.33490.31860.30330.28880.27510.26210.24990.23830.22740.21700.207270.35380.33320.31390.29590.27910.26330.24860.23480.22180.20970.19830.18770.17760.16820.159480.30500.28480.26600.24870.23260.21760.20380.19090.17890.16780.15740.14780.13880.13040.122

36、690.26300.24340.22550.20900.19380.17990.16700.15520.14430.13420.12490.11640.10840.10110.0943100.22670.20800.19110.17560.16150.14860.13690.12620.11640.10740.09920.09160.08470.07840.0725110.19540.17780.16190.14760.13460.12280.11220.10260.09380.08590.07870.07210.06620.06070.0558120.16850.15200.13720.12

37、400.11220.10150.09200.08340.07570.06870.06250.05680.05170.04710.0429130.14520.12990.11630.10420.09350.08390.07540.06780.06100.05500.04960.04470.04040.03650.0330140.12520.11100.09850.08760.07790.06930.06180.05510.04920.04400.03930.03520.03160.02830.0254150.10790.09490.08350.07360.06490.05730.05070.04

38、480.03970.03520.03120.02770.02470.02190.0195160.09300.08110.07080.06180.05410.04740.04150.03640.03200.02810.02480.02180.01930.01700.0150170.08020.06930.06000.05200.04510.03910.03400.02960.02580.02250.01970.01720.01500.01320.0116180.06910.05920.05080.04370.03760.03230.02790.02410.02080.01800.01560.01

39、350.01180.01020.0089190.05960.05060.04310.03670.03130.02670.02290.01960.01680.01440.01240.01070.00920.00790.0068200.05140.04330.03650.03080.02610.02210.01870.01590.01350.01150.00980.00840.00720.00610.0053210.04430.03700.03090.02590.02170.01830.01540.01290.01090.00920.00780.00660.00560.00480.0040220.

40、03820.03160.02620.02180.01810.01510.01260.01050.00880.00740.00620.00520.00440.00370.0031230.03290.02700.02220.01830.01510.01250.01030.00860.00710.00590.00490.00410.00340.00290.0024240.02840.02310.01880.01540.01260.01030.00850.00700.00570.00470.00390.00320.00270.00220.0018250.02450.01970.01600.01290.

41、01050.00850.00690.00570.00460.00380.00310.00250.00210.00170.0014300.01160.00900.00700.00540.00420.00330.00260.00200.00160.00120.00100.00080.00060.00050.0004附錄三：一元年金終值系數(shù)表 F=(1+i)n-1/in1%2%3%4%5%6%7%8%9%10%11%12%13%14%15%11.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.

42、00001.000022.01002.02002.03002.04002.05002.06002.07002.08002.09002.10002.11002.12002.13002.14002.150033.03013.06043.09093.12163.15253.18363.21493.24643.27813.31003.34213.37443.40693.43963.472544.06044.12164.18364.24654.31014.37464.43994.50614.57314.64104.70974.77934.84984.92114.993455.10105.20405.30

43、915.41635.52565.63715.75075.86665.98476.10516.22786.35286.48036.61016.742466.15206.30816.46846.63306.80196.97537.15337.33597.52337.71567.91298.11528.32278.53558.753777.21357.43437.66257.89838.14208.39388.65408.92289.20049.48729.783310.089010.404710.730511.066888.28578.58308.89239.21429.54919.897510.

44、259810.636611.028511.435911.859412.299712.757313.232813.726899.36859.754610.159110.582811.026611.491311.978012.487613.021013.579514.164014.775715.415716.085316.78581010.462210.949711.463912.006112.577913.180813.816414.486615.192915.937416.722017.548718.419719.337320.30371111.566812.168712.807813.486

45、414.206814.971615.783616.645517.560318.531219.561420.654621.814323.044524.34931212.682513.412114.192015.025815.917116.869917.888518.977120.140721.384322.713224.133125.650227.270729.00171313.809314.680315.617816.626817.713018.882120.140621.495322.953424.522726.211628.029129.984732.088734.35191414.947

46、415.973917.086318.291919.598621.015122.550524.214926.019227.975030.094932.392634.882737.581140.50471516.096917.293418.598920.023621.578623.276025.129027.152129.360931.772534.405437.279740.417543.842447.58041617.257918.639320.156921.824523.657525.672527.888130.324333.003435.949739.189942.753346.671750.980455.71751718.430420.01