複利終值

複利終值

複利是計算利息的一種方法。按照這種方法,每經過一個計息期,要將所生利息加入本金再計利息,逐期滾算,俗稱“利滾利”。這裡所說的計息期是指相鄰兩次計息的時間間隔,如年、月、日等。除非特別指明,計息期為1年。所謂"複利",實際上就是我們通常所說的"利滾利"。即每經過一個計息期,要將利息加入本金再計利息,逐期計算。終值是指最後得到的數據。 因此,複利終值就是指一筆收支經過若干期後再到期時的金額,這個金額和最初的收支額事實上具有相同的支付能力。

定義

要了解複利終值,必須先了解單利。

單利是在任一個計息期均僅按照初始資本計算利息,而不計算到期利息的利息的一種計息方式。銀行存款多用這種計息方式。公式為:

複利終值 複利終值

相對的,複利是在任一個計息期均按照本息和計算利息,而僅不計算初始資金的利息的一種計息方式。銀行貸款多用這種計息方式。公式為:

複利終值 複利終值
複利終值 複利終值
複利終值 複利終值

上述是計算複利終值的一般公式,其中的被稱為複利終值係數或1元的複利終值,用符號(F/P,i,n)表示。例如,(F/P,6%,3)表示利率為6%的3期複利終值的係數。為了便於計算,可編制“複利終值係數表”備用。該表的第一行是利率i,第一列是計息期數n,相應的值在其縱橫相交處。通過該表可以查出,(S/P,6%,3)=1.1910(保留四位小數的近似值)。在時間價值為6%的情況下,存入時的1元和3年後的1.1910元在經濟上是等效的,根據這個係數可以把現值換算成終值。

公式

公式推導:根據複利的概念,計算某一筆錢的終值,可用以下公式計算:

複利終值 複利終值

但是由於這樣計算的話,如果期限太長的話,這個累加計算是非常麻煩的,因此,我們通常把公式簡化、因式分解為:

複利終值 複利終值
複利終值 複利終值

而其中提取掉x後的冪指數稱為複利終值係數。

示例

實例一

例:張三擬投資10萬元於一項目,該項目的投資期為5年,每年的投資報酬率為20%,張三盤算著:這10萬元本金投入此項目後,5年後可以收回的本息合計為多少?

分析:由於貨幣隨時間的增長過程與複利的計算過程在數學上是相似的,因此,在計算貨幣的時間價值時,可以使用複利計算的各種方法。張三的這筆賬實際上是關於"複利終值"的計算問題。

假如張三在期初投入資金100000元,利息用i表示,那么:

經過1年的時間後,張三的本利和

複利終值 複利終值
複利終值 複利終值
複利終值 複利終值
複利終值 複利終值
複利終值 複利終值

(元)

經過2年的時間後,張三的本利和

複利終值 複利終值
複利終值 複利終值
複利終值 複利終值
複利終值 複利終值
複利終值 複利終值
複利終值 複利終值

(元)

依次類推,5年後,張三的本利和

複利終值 複利終值
複利終值 複利終值
複利終值 複利終值
複利終值 複利終值
複利終值 複利終值

(元)

我們稱(1+i)n為複利終值係數,在實際運用時,通常查表得到其解。查複利終值表,得知當i=20%,n=5時,複利終值係數為2.4883,那么5年後張三的本利和=100000×2.4883=248830元。當然,之所以係數表中的係數使用時與直接的冪指數計算結果有微小的差異,那是因為係數表中的係數不可能每一個係數精確到它的最後一位小數位,而是保留至多4位小數。

複利終值 複利終值

S為複利終值 P為複利現值 i為年收益率或利率 n為投資期限

實例二

例如,某人將10000元投資於一項事業,年報酬率為6%。按單利計算:

經過1年時間的期終金額為:

複利終值 複利終值
複利終值 複利終值
複利終值 複利終值
複利終值 複利終值

=10600(元)

其中:P——現值或初始值;

i——報酬率或利率;

S——終值或本利和。

若此人不提走現金,則第2年本利和為:

複利終值 複利終值
複利終值 複利終值
複利終值 複利終值
複利終值 複利終值

=11200(元)

同理,第3年的期終金額為:

複利終值 複利終值
複利終值 複利終值
複利終值 複利終值
複利終值 複利終值

=11800(元)

……

仍以上例為例,按複利計算:

經過1年時間的期終金額為:

複利終值 複利終值
複利終值 複利終值
複利終值 複利終值

=10600(元)

若此人不提走現金,則第2年本利和為:

複利終值 複利終值
複利終值 複利終值
複利終值 複利終值

=11236(元)

同理,第3年的期終金額為:

複利終值 複利終值
複利終值 複利終值
複利終值 複利終值

=11910.16(元)

……

C語言計算

#include "stdio.h"

#include <math.h>

void main()

{

float p,s,x,z,n;

float i;

printf("輸入現金回車輸入收益率回車輸入投資年限回車\n");

scanf("%f%f%f",&p,&i,&x);//您投資了多少現金%d,您的年收益率是多少%d,您的投資了多少年

n=1+i;

z=(float)(pow(n,x));

s=p*z;

printf("您的現金終值為%f",s);

}

係數表

本詞條提供1%~50%利率1~50期的複利終值係數(精確到萬分位)供查詢。但因利率越高、期數越長,會導致數據過長,所以本表特意每5個百分點分出一張表格,合計10張表格,以免係數出現表內換行的情形。

表一(1%~5%利率)

複利終值係數表
利息 —— 期數1%2%3%4%5%
11.01001.02001.03001.04001.0500
21.02011.04041.06091.08161.1025
31.03031.06121.09271.12491.1576
41.04061.08241.12551.16991.2155
51.05101.10411.15271.21671.2763
61.06151.12621.19411.26531.3401
71.07211.14871.22991.31591.4071
81.08291.17171.26681.36861.4775
91.09371.19511.30481.42331.5513
101.10461.21901.34391.48021.6289
111.11571.24341.38421.53951.7103
121.12681.26841.42581.60101.7959
131.13811.29361.46851.66511.8856
141.14951.31951.51261.73171.9799
151.16101.34591.55801.80092.0789
161.17261.37281.60471.87302.1829
171.18433.40021.65281.94792.2920
181.19611.42821.70242.02582.4066
191.20811.45681.75352.10682.5270
201.22021.48591.80612.19112.6533
211.23241.51571.86032.27882.7860
221.24471.54601.91612.36992.9253
231.25721.57691.97352.46473.0715
241.26971.60842.03282.56333.2251
251.28241.64062.09382.66583.3864
261.29531.67342.15662.77253.5557
271.30821.70692.22132.88343.7335
281.32131.74102.28792.99873.9201
291.33451.77582.35663.11874.1161
301.34781.81142.42733.24344.3219
311.36131.84762.50013.37314.5380
321.37491.88452.57513.50814.7649
331.38871.92222.65233.64845.0032
341.40261.96072.73193.79435.2533
351.41661.99992.81393.94615.5160
361.43082.03992.89834.10395.7918
371.44512.08072.98524.26816.0814
381.45952.12233.07484.43886.3855
391.47412.16473.16704.61646.7048
401.48892.20803.26204.80107.0400
411.50382.25223.35994.99317.3920
421.51882.29723.46075.19287.7616
431.53402.34323.56455.40058.1500
441.54932.39013.67155.61658.5572
451.56482.43793.78165.84128.9850
461.58052.48663.89506.07489.4343
471.59632.53634.01196.31789.9060
481.61222.58714.13236.570510.4013
491.62832.63884.25626.833310.9213
501.64462.69164.38397.106711.4674

表二(6%~10%利率)

複利終值係數表(續表一)
利率 —— 期數6%7%8%9%10%
11.06001.07001.08001.09001.1000
21.12361.14491.16641.18811.2100
31.19101.22501.25971.29501.3310
41.26251.31081.36051.41161.4641
51.33821.40261.46931.53861.6105
61.41851.50071.58691.67711.7716
71.50361.60581.71381.82801.9487
81.59381.71821.85091.99262.1436
91.68951.83851.99902.17192.3579
101.79081.96722.15892.36742.5937
111.89832.10492.33162.58042.8531
122.01222.25222.51822.81273.1384
132.13292.40982.71963.06583.4522
142.26092.57852.93723.34173.7975
152.39662.75903.17223.64254.1772
162.54042.95223.42593.97034.5950
172.69283.15883.70004.32765.0545
182.85433.37993.99604.71715.5599
193.02563.61654.31575.14176.1159
203.20713.86974.66105.60446.7275
213.39964.14065.03386.10887.4002
223.60354.43045.43656.65868.1403
233.81984.74055.87157.25798.9543
244.04895.07246.34127.91119.8497
254.29195.42746.84858.623110.8347
264.54945.80747.39649.399211.9182
274.82236.21397.988110.245113.1100
285.11176.64888.627111.167114.4210
295.41847.11439.317312.172215.8631
305.74357.612310.062713.267717.4494
316.08818.145110.867714.461819.1943
326.45348.715311.737115.763321.1138
336.84069.325312.676017.182023.2252
347.25109.978113.690118.728425.5477
357.686110.676614.785320.414028.1024
368.147311.423915.968222.251230.9127
378.636112.223617.245624.253834.0039
389.154313.079318.625326.436737.4043
399.703513.994820.115328.816041.1448
4010.285714.974521.724531.409445.2593
4110.902916.022723.462534.236349.7852
4211.557017.144325.339537.317554.7637
4312.250518.344427.366640.676160.2401
4412.985519.628529.556044.337066.2641
4513.764621.002531.920448.327372.8905
4614.590522.472634.474152.676780.1795
4715.465924.045737.232057.417688.1975
4816.393925.728940.210662.585297.0172
4917.377527.529943.427468.2179106.7190
5018.420229.457046.901674.3575117.3909

表三(11%~15%利率)

複利終值係數表(續表二)
利率 —— 期數11%12%13%14%15%
11.11001.12001.13001.14001.1500
21.23211.25441.27691.29961.3225
31.36761.40491.44291.48151.5209
41.51811.57351.63051.68901.7490
51.68511.76231.84241.92542.0114
61.87041.97382.08202.19502.3131
72.07622.21072.35262.50232.6600
82.30452.47602.65842.85263.0590
92.55802.77313.00403.25193.5179
102.83943.10583.39463.70724.0456
113.15183.47853.83594.22624.6524
123.49853.89604.33454.81795.3503
133.88334.36354.89805.49246.1528
144.31044.88715.53486.26137.0757
154.78465.47366.25437.13798.1371
165.31096.13047.06738.13729.3576
175.89516.86607.98619.276510.7613
186.54367.69009.024310.575212.3755
197.26338.612810.197412.055714.2318
208.06239.646311.523113.743516.3665
218.949210.803813.021115.667618.8215
229.933612.100314.713817.861021.6447
2311.026313.552316.626620.361624.8915
2412.239215.178618.788123.212228.6252
2513.585517.000121.230526.461932.9190
2615.079919.040123.990530.166637.8568
2716.738621.324927.109334.389943.5353
2818.579923.883930.633539.204550.0656
2920.623726.749934.615844.693157.5755
3022.892329.959939.115950.950266.2118
3125.410433.555144.201058.083276.1435
3228.205637.581749.947166.214887.5651
3331.308242.091556.440275.4849100.6998
3434.752147.142563.777486.0528115.8048
3538.574952.799672.068598.1002133.1755
3642.818159.135681.4374111.8342153.1519
3747.528166.231892.0243127.4910176.1246
3852.756274.1797103.9874145.3397202.5433
3958.559383.0812117.5058165.6873232.9248
4065.000993.0510132.7816188.8835267.8635
4172.1510104.2171150.0432215.3272308.0431
4280.0876116.2314169.5488245.4730354.2495
4388.8972130.7299191.5901279.8392407.3870
4498.6759146.4175216.4968319.0167468.4950
45109.5302163.9876244.6414363.6791538.7693
46121.5786183.6661276.4448414.5941619.5847
47134.9522205.7061312.3826472.6373712.5224
48149.7970230.3908352.9923538.8065819.4007
49166.2746258.0377398.8813614.2395942.3108
50184.5648289.0022450.7359700.23301,083.6574

表四(16%~20%利率)

複利終值係數表(續表三)
利率 —— 期數16%17%18%19%20%
11.16001.17001.18001.19001.2000
21.34561.36891.39241.41611.4400
31.56091.60161.64301.68521.7280
41.81061.87391.93882.00532.0736
52.10032.19242.28782.38642.4883
62.43642.56522.69962.83982.9860
72.82623.00123.18553.37933.5832
83.27843.51153.75894.02144.2998
93.80304.10844.43554.78545.1598
104.41144.80685.23385.69476.1917
115.11735.62406.17596.77677.4301
125.93606.58017.28768.06428.9161
136.88587.69878.59949.596410.6993
147.98759.007510.147211.419812.8392
159.265510.538711.973713.589515.4070
1610.748012.330314.129016.171518.4884
1712.467714.426516.672219.244122.1861
1814.462516.879019.673322.900526.6233
1916.776519.748423.214427.251631.9480
2019.460823.105627.393032.429438.3376
2122.574527.033632.323838.591046.0051
2226.186431.629338.142145.923355.2061
2330.376237.006245.007654.648766.2474
2435.236443.297353.109065.032079.4968
2540.874250.657862.668677.388195.3962
2647.414159.269773.949092.0918114.4755
2755.000469.345587.2598109.5893137.3706
2863.800481.1342102.9666130.4112164.8447
2974.008594.9271121.5005155.1893197.8136
3085.8499111.0647143.3706184.6753237.3763
3199.5859129.9456169.1774219.7636284.8516
32115.5196152.0364199.6293261.5187341.8219
33134.0027177.8826235.5625311.2073410.1863
34155.4432208.1226277.9638370.3366492.2235
35180.3141243.5035327.9973440.7006590.6682
36209.1643284.8991387.0368524.4337708.8019
37242.6306333.3319456.7034624.0761850.5623
38281.4515389.9983538.9100742.65061,020.6747
39326.4838456.2980635.9139883.75421,224.8096
40378.7212533.8687750.37831,051.66751,469.7716
41439.3165624.6264885.44641,251.48431,763.7259
42509.6072730.81291,044.82681,489.26642,116.4711
43591.1443855.05111,232.89561,772.22702,539.7653
44685.72741,000.40981,454.81682,108.95013,047.7183
45795.44381,170.47941,716.68392,509.65063,657.2620
46922.71481,369.46092,025.68702,986.48424,388.7144
471,070.34921,602.26922,390.31063,553.91625,266.4573
481,241.60511,874.65502,820.56654,229.16036,319.7487
491,440.26192,193.34643,328.26855,032.70087,583.6985
501,670.70382,566.21533,927.35695,988.91399,100.4182

表五(21%~25%利率)

複利終值係數表(續表四)
利率 —— 期數21%22%23%24%25%
11.21001.22001.23001.24001.2500
21.46411.48841.51291.53761.5625
31.77161.81581.86091.90661.9531
42.14362.21532.28892.36422.4414
52.59372.70272.81532.93163.0518
63.13843.29733.46283.63523.8147
73.79754.02274.25934.50774.7684
84.59504.90775.23895.58955.9605
95.55995.98746.44396.93107.4506
106.72757.30467.92598.59449.3132
118.14038.91179.748910.657111.6415
129.849710.872211.991213.214814.5519
1311.918213.264114.749116.386318.1899
1414.421016.182218.141420.319122.7374
1517.449419.742322.314025.195628.4217
1621.113824.085627.446231.242635.5271
1725.547729.384433.758838.740844.4089
1830.912735.849041.523348.038655.5112
1937.404343.735851.073759.567969.3889
2045.259353.357662.820673.864186.7362
2154.763765.096377.269491.5915108.4202
2266.264179.417595.0413113.5735135.5253
2380.179596.8893116.9008140.8312169.4066
2497.0172118.2050143.7880174.6306211.7582
25117.3909144.2101176.8593216.5420264.6978
26142.0429175.9364217.5369268.5121330.8722
27171.8719214.6424267.5704332.9550413.5903
28207.9651261.8637329.1115412.8642516.9879
29251.6377319.4737404.8072511.9516646.2349
30304.4816389.7579497.9129634.8199807.7936
31368.4228475.5046612.4328787.17671,009.7420
32445.7916580.1156753.2924976.09911,262.1774
33539.4078707.7411926.54961,210.36291,577.7218
34652.6834863.44411,139.65601,500.85001,972.1523
35789.74701,053.40181,401.77691,861.05402,465.1903
36955.59381,285.15021,724.18562,307.70703,081.4879
371,156.26851,567.88332,120.74832,861.55673,851.8599
381,399.08491,912.81762,608.52043,548.33034,814.8249
391,692.89272,333.63753,208.48014,399.92956,018.5311
402,048.40022,847.03783,946.43055,455.91267,523.1638
412,478.56433,473.38614,854.10956,765.33179,403.9548
422,999.06284,237.53105,970.55478,389.011311,754.9435
433,628.86595,169.78787,343.782310,402.374014,693.6794
444,390.92786,307.14119,032.852212,898.943718,367.0992
455,313.02267,694.712211,110.408215,994.690222,958.8740
466,428.75749,387.548913,665.802119,833.415828,698.5926
477,778.796411,452.809616,808.936524,593.435635,873.2407
489,412.343713,972.427720,674.992030,495.860244,841.5509
4911,388.935817,046.361925,430.240137,814.866656,051.9386
5013,780.612320,796.561531,279.195346,890.434670,064.9232

表六(26%~30%利率)

複利終值係數表(續表五)
利率 —— 期數26%27%28%29%30%
11.26001.27001.28001.29001.3000
21.58761.61291.68341.66411.6900
32.00042.04842.09722.14672.1970
42.52052.60142.68442.76922.8561
53.17583.30383.43603.57233.7129
64.00154.19594.39804.60834.8268
75.04195.32885.62955.94476.2749
86.35286.76757.20587.66868.1573
98.00458.59479.22349.892510.6045
1010.085710.915311.805912.761413.7858
1112.708013.862515.111616.462217.9216
1216.012017.605319.342821.236223.2981
1320.175222.358824.758827.394730.2875
1425.420728.395731.691335.339139.3738
1532.030136.062540.564845.587551.1859
1640.357945.799451.923058.807966.5417
1750.851058.165266.461475.862186.5042
1864.072273.869885.070697.8622112.4554
1980.731093.8147108.8904126.2422146.1920
20101.7211119.1446139.3797162.8524190.0496
21128.1685151.3137178.4060210.0796247.0645
22161.4624192.1683228.3596271.0027321.1839
23203.4804244.0538292.3003349.5935417.5391
24256.3853309.0483374.1444450.9756542.8008
25323.0454393.6344478.9049581.7585705.6410
26407.0373499.9157612.9982750.4685917.3333
27512.8670634.8929784.6377968.10441,192.5333
28646.2124806.31401,004.33631,248.85461,550.2933
29814.22761,024.01871,285.55041,611.02252,015.3813
301,025.92671,300.50381,645.50462,078.21902,619.9956
311,292.66771,651.63982,106.24582,680.90253,405.9943
321,628.76132,097.58262,695.99473,458.36424,427.7926
332,052.23922,663.92993,450.87324,461.28985,756.1304
342,585.82153,383.19104,417.11775,755.06397,482.9696
353,258.13504,296.65255,653.91067,424.03249,727.8604
364,105.25015,456.74877,237.00569,577.001812,646.2186
375,172.61526,930.07099,263.367112,354.332416,440.0841
386,517.49518,801.190011,857.109915,937.088821,372.1094
398,212.043811,177.511315,177.100720,558.844527,783.7422
4010,347.175314,195.439319,426.688926,520.909436,118.8648
4113,037.440818,028.208024,866.161834,211.973146,954.5243
4216,427.175422,895.824131,828.687144,133.445361,040.8815
4320,698.241029,077.696640,740.719556,932.144579,353.1460
4426,079.783736928.674752,148.121073,442.4664103,159.0898
4532,860.527546,899.416966,749.594994,740.7816134,106.8167
4641,404.264659,562.259485,439.4814122,215.6083174,338.8617
4752,169.373475,644.0695109,362.5362157,658.1347226,640.5202
4865,733.410596,067.9683139,984.0464203,378.9938294,632.6763
4982,824.0972122,006.3197179,179.5794262,358.9020383,022.4792
50104,358.3625154,948.0260229,349.8616338,442.9836497,929.2230

表七(31%~35%利率)

複利終值係數表(續表六)
利率 —— 期數31%32%33%34%35%
11.31001.32001.33001.34001.3500
21.71611.74241.76891.79561.8225
32.24812.29992.35262.40612.4604
42.94503.03603.12903.22423.3215
53.85794.00754.16164.32044.4840
65.05395.28995.53495.78936.0534
76.62066.98267.36147.75778.1722
88.67309.21709.790710.395311.0324
911.361712.166513.021613.929714.8937
1014.883816.059817.318718.665920.1066
1119.497721.198923.033925.011327.1439
1225.542027.982530.635133.516436.6442
1333.460136.937040.744744.912049.4697
1443.832748.756854.190560.182166.7841
1557.420864.359072.073380.644090.1585
1675.221384.953895.8575108.0629121.7139
1798.5399112.1390127.4905144.8043164.3138
18129.0872148.0235169.5624194.0378221.8236
19169.1043195.3911225.5180260.0107299.4619
20221.5266257.9162299.9389348.4143404.2736
21290.1999340.4494398.9188466.8752545.7693
22380.1618449.3932530.5620625.6127736.7886
23498.0120593.1990705.6474838.3210994.6646
24652.3957783.0227938.51101,123.35021,342.7973
25854.63841,033.59001,248.21971,505.28921,812.7763
261,119.57631,364.33871,660.13222,017.08762,447.2480
271,466.64491,800.92712,207.97582,702.89743,303.7848
281,921.30482,377.22382,936.60783,621.88254,460.1095
292,516.90933,137.93543,905.68844,853.32256,021.1478
303,297.15124,142.07485,194.56556,503.45228,128.5495
314,319.26815,467.53876,908.77228,714.625910,973.5418
325,658.24137,217.15119,188.667011,677.598714,814.2815
337,412.29609,526.639512,220.927115,647.982319,999.2800
349,710.107812,575.164116,253.833020,968.296326,999.0280
3512,720.241216,599.216621,617.597928,097.517036,448.6878
3616,663.516021,910.965928,751.405237,650.672849,205.7285
3721,829.206028,922.475038,239.368950,451.901566,427.7335
3828,596.259938,177.667050,858.360667,705.548189,677.4402
3937,461.100450,394.520567,641.619690,591.4344121,064.5442
4049,074.041566,520.767089,963.3541121,392.5221163,437.1347
4164,286.994487,807.4125119,651.2609162,665.9796220,640.1318
4284,215.9627115,905.7845159,136.1770217,972.4127297,864.1780
43110,322.9111152,995.6355211,651.1154292,083.0330402,116.6402
44144,523.0136201,954.2388281,495.9835391,391.2642542,857.4643
45189,325.1478266,579.5953374,389.6581524,464.2940732,857.5768
46248,015.9436351,885.0658497,938.2452702,782.1540989,357.7287
47324,900.8861464,488.2868662,257.8662941,728.08641,335,632.9338
48425,620.1608614,124.5386880,802.96201,261,915.63581,803,104.4606
49557,562.4107809,324.39091,171,467.93941,690,966.95192,434,191.0218
50730,406.75801,068,308.19601,558,052.35942,265,895.71563,286,157.8794

表八(36%~40%利率)

複利終值係數表(續表七)
利率 —— 期數36%37%38%39%40%
11.36001.37001.38001.39001.4000
21.84961.87691.90441.93211.9600
32.51552.57142.62812.68562.7440
43.42103.52283.62673.73303.8416
54.65264.82625.00495.18895.3782
66.32756.61196.90687.21257.5295
78.60549.05829.531310.025410.5414
811.703412.409813.153213.935414.7579
915.916617.001418.151519.370220.6610
1021.646623.291925.049026.924528.9255
1129.439331.910034.567737.425140.4957
1240.037543.716647.703452.020956.6939
1354.451059.891865.830672.309079.3915
1474.053582.051790.8463100.5095111.1201
15100.7126112.4109125.3679139.7082155.5681
16136.9691154.0030173.0077194.1944217.7953
17186.2779210.9841238.7506269.9303304.9135
18253.3380289.0482329.4758375.2031426.8789
19344.5396395.9960454.6766521.5323597.6304
20468.5740542.5145627.4538724.9299836.6826
21637.2606743.2449865.88621,007.65251,171.3556
22866.67441,018.24541,194.92291,400.63701,639.8978
231,178.67721,394.99631,648.99371,946.88552,295.8569
241,603.00101,911.14492,275.61132,706.17083,214.1997
252,180.08132,618.26853,761.57743,761.57744,499.7958
262,964.91073,587.02784,333.67415,228.59266,299.8314
274,032.27864,914.22815,980.47027,267.74388,819.7640
285,483.89886,732.49258,253.048910,102.163812,347.6696
297,458.10249,223.515011,389.207514,042.007717,286.7374
3010,143.019212,636.2153·15,717.106419,518.390724,201.4323
3113,794.506217,311.614921,689.606827,130.563133,882.0053
3218,760.528523,716.912429,931.657437,711.482747,434.8074
3325,514.318732,492.170041,305.687152,418.961066,408.7304
3434,699.473544,514.272857,001.848372,862.355892,972.2226
3547,191.283960,984.553878,662.5506101,278.6745130,161.1116
3664,180.146183,548.8387108,554.3198140,777.3576182,225.5562
3787,284.9987114,461.9090149,804.9613195,680.5270255,115.7786
38118,707.5982156,812.8153206,730.8466271,995.9326357,162.0901
39161,442.3336214,833.5570285,288.5684378,074.3463500,026.9261
40219,561.5736294,321.9731393,698.2244525,523.3413700,037.6966
41298,603.7402403,221.1031543,303.5496730,477.4445980,052.7752
42406,101,0866552,412.9113749,758.89851,015,363.64781,372,073.8853
43552,297.4778756,805.68841,034,667.28001,411,355.47041,920,903.4394
44751,124.56981,036,823.79321,427,840.84621,961,784.10392,689,264.8152
451,029,529.41491,420,448.59661,970,420.36782,726,879.90443,764,970.7413
461,389,280.00431,946,014.57742,719,180.10753,790,363.06725,270,959.0378
471,889,420.85092,666,039.97103,752,468.54845,268,604.66347,379,342.6530
482,569,612.29603,652,474.76035,178,406.59687,323,360.482110,331,079.7142
493,494,672.72255,003,890.42157,146,201.103510,179,471.070114,463,511.5998
504,752,754.90276,855,329.87759,861,757.522914,149,464.787420,248,916.239

表九(41%~45%利率)

複利終值係數表(續表八)
利率 —— 期數41%42%43%44%45%
11.41001.42001.43001.44001.4500
21.98812.01642.04492.07362.1025
32.80322.86332.92422.98603.0486
43.95254.06594.18164.29984.4205
55.57315.77355.97976.19176.4097
67.85808.19848.55108.91619.2941
711.07988.551012.227912.839213.4765
815.622616.531317.485918.488419.5409
922.027823.474425.004926.623328.3342
1031.059333.333735.756938.337641.0847
1143.739647.333851.132455.206159.5728
1261.748967.214173.119479.496886.3806
1387.066095.4440104.5607114.4755125.2518
14122.7630135.5304149.5218164.8447181.6151
15173.0959192.4532213.8162237.3763263.3419
16244.0652273.2836305.7571341.8219381.8458
17344.1319388.0627437.2327492.2235553.6764
18485.2260551.0490625.2428708.8019802.8308
19684.1686782.4895894.09721,020.67471,164.1047
20964.67771,111.13511,278.55891,469.77161,687.9518
211,360.19561,577.81191,828.33932,116.47112,447.5301
221,917.87582,240.49292,614.52523,047.71833,548.9187
232,704.20493,181.50003,738.77104,388.71445,145.9321
243,812.92894,517.72995,346.44256,319.78477,461.6015
255,376.22976,415.17657,645.41289,100.438210,819.3222
267,580.48399,109.550610,932.940213,104.630915,688.0173
2710,688.482312,935.561915,634.104518,870.668622,747.6250
2815,070.760018,368.497922,356.769527,173.762732,984.0563
2921,249.771626,083.267031,970.180439,130.218347,826.8816
3029,962.178037,038.239245,717.357956,347.514469,348.9783
3142,246.671052,594.299665,375.821881,140.4207100,556.0185
3259,567.806174,683.905493,487.4252116,842.2058145,806.2269
3383,990.6066106,051.1457133,687.0181168,252.7762211,419.0289
34118,426.7552150,592.6269191,172.4358242,283.9979306,557.5920
35166,981.7249213,841.5302273,376.5833348,888.9569444,508.5083
36235,444.2321303,654.9728390,928.5141502,400.0980644,537.3371
37331,976.3673431,190.0614559,027.7751723,456.1411934,579.1388
38468,086.6778612,289.8872799,409.71841,041,776.84321,355,139.7513
39660,002.2158869,451.63991,143,155.89731,500,158.65421,964,952.6393
40930,603.12421,234,621.32861,634,712.93322,160,228.46202,849,181.3270
411,312,150.40521,753,162.28662,337,639.49453,110,728.98534,131,312.9242
421,850,132.07132,489,490.44703,342,824.47714,479,449.73885,990,403.7400
432,608,686.22053,535,076.43484,780,239.00226,450,407.62398,686,085.4230
443,678,247.57095,019,808.53746,835,741.77329,288,586.978412,594,823.8634
455,186,329.07507,128,128.12319,775,110.735713,375,565.248918,262,494.6019
467,312,623.995710,121,941.934813,978,408.352019,260,813.958526,480,617.1729
4710,310,940.833914,373,157.547419,989,123.943427,735,572.100138,396,894.9007
4814,538,426.575820,409,883.717328,584,447.239039,939,223.824255,675,497.6060
4920,499,181.471928,982,034.878640,875,759.551657,512,482.306980,729,471.5287
5028,903,845.875441,154,489.527658,452,336.159182,817,974.5219117,057,733.7166

表十(46%~50%利率)

複利終值係數表(續表九)
利率 —— 期數46%47%48%49%50%
11.46001.47001.48001.49001.5000
22.13162.16092.19042.22012.2500
33.11213.17653.24183.30793.3750
44.54374.66954.79794.92885.5625
56.63386.86417.10087.34407.5938
69.685410.090310.509210.942511.3906
714.140714.832715.553716.304417.0859
820.645421.804123.019424.293525.6289
930.142332.052134.068736.197338.4434
1044.007747.116550.421753.934057.6650
1164.251269.261374.624180.361786.4976
1293.8068101.8141110.4436119.7389129.7463
13136.9579149.6668163.4565178.4109194.6195
14199.9586220.0101241.9157265.8323291.9293
15291.9395323.4149358.0352396.0901437.8939
16426.2316475.4199529.8921590.1743656.8408
17622.2982698.8673784.2403879.3597985.2613
18908.55541,027.33491,160.67571,310.24601,477.8919
191,326.49091,510.18221,717.80001,952.26652,216.8378
201,936.67662,219.96792,542.34402,908.87713,325.2567
212,824.54793,263.35283,762.66914,334.22684,987.8850
224,128.21994,797.12865,568.75026,457.99807,481.8276
236,027.20117,051.77918,241.75039,622.417011,222.7415
248,799.713610,366.115312,197.790514,337.401316,834.1122
2512,847.581915,238.189518,052.729921,362.728025,251.1683
2618,757.469622,400.138526,718.040331,830.464737,876.7524
2727,385.905632,928.238639,542.699647,427.392456,815.1287
2839,983.422148,404.459358,523.195470,666.814685,222.6930
2958,375.796371,154.555186,614.3292105,293.5538127,834.0395
3085,228.6626104,597.1960128,189.2073156,887.3952191,751.0592
31124,433.8474153,757.8782189,720.0268233,762.2188287,626.5888
32181,673.4172226,024.0809280,785.6396348,305.7060431,439.8833
33265,243.1891332,255.3989415,562.7466518,975.5019647,159.8249
34387,255.0561488,415.4364615,032.8650773,273.4979970,739.7374
35565,382.3818717,970.6916910,248.64021,152,177.51181,456,109.6060
36825,472.87751,055,416.91661,347,167.98751,716,744.49262,184,164.4091
371,205,190.40111,551,462.86741,993,808.62152,557,949.29403,276,246.6136
381,759,577.98562,280,650.41512,950,836.75983,811,344.44814,914,369.9204
392,568,983.85903,352,556.11024,367,238.40455,678,903.22777,371,554.8806
403,750,716.43424,928,257.48216,463,512.83878,461,565.809311,057,332.3209
415,476,045.99397,244,538.49869,565,999.001212,607,733.055816,585,998.4814
427,995,027.151110,649,471.593014,157,678.521818,785,522.253124,878,997.7221
4311,672,739.640515,654,723.241720,953,364.212327,990,428.157237,318,496.5832
4417,042,199.875223,012,443.165231,010,979.034241,705,737.954255,977,744.8747
4524,881,611.817733,828,291.452945,896,248.970662,141,549.551783,966,617.3121
4636,327,153.253949,727,588.435767,926,448.476592,590,908.8321125,949,925.9681
4753,037,643.750773,099,555.0007100,531,143.7453137,960,454.1598188,924,888.9522
4877,434,959.8762107,456,345.8511148,786,092.7430205,561,076.6982283,387,333.4283
49113,055,041.4189157,960,828.4011220,203,417.2597306,286,004.2803425,081,000.1424
50165,060,360.4716232,202,417.7496325,901,057.5443456,050,366.3776637,621,500.2135

插值法

概念

插值法,是指在係數表中找不到對應利率,但想知道對應利率時利用的一種求名義利率的方法。之所以說求得的是名義利率而非實際利率,是因為在求這個利率時沒有(也無法)考慮通貨膨脹率、貨幣實際貶值率等因素的數據。

公式

複利終值 複利終值

這樣可以立即知道所求的利率。

套用

假設老張投入資金150000元進行理財,希望獲得額外收益250000元。該筆投資期限為5年,按年計息,那么老張期望的終值係數應該不低於:

複利終值 複利終值

則老張期望的年化收益率應該不低於:

複利終值 複利終值
複利終值 複利終值
複利終值 複利終值
複利終值 複利終值

求得利率(這裡就是年化收益率)i的值至少為,即,得出,換句話說,老張的理財投資的年化收益率不得低於21.67%(保留四位小數),否則老張是不願意去做這一理財產品的。

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