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。

基本介紹

  • 中文名：複利終值
  • 外文名：複利終值
  • 所謂："複利"
  • 方法：計算利息
定義,公式,示例,實例一,實例二,C語言計算,係數表,插值法,概念,公式,套用,

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：
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：
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：
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：
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
（元）
經過2年的時間後，張三的本利和
（元）
依次類推，5年後，張三的本利和
（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。
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：
=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：
=11200(元)
同理，第3年的期終金額為：
=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：
=10600（元）
若此人不提走現金，則第2年本利和為：
=11236（元）
同理，第3年的期終金額為：
=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%
1
1.0100
1.0200
1.0300
1.0400
1.0500
2
1.0201
1.0404
1.0609
1.0816
1.1025
3
1.0303
1.0612
1.0927
1.1249
1.1576
4
1.0406
1.0824
1.1255
1.1699
1.2155
5
1.0510
1.1041
1.1527
1.2167
1.2763
6
1.0615
1.1262
1.1941
1.2653
1.3401
7
1.0721
1.1487
1.2299
1.3159
1.4071
8
1.0829
1.1717
1.2668
1.3686
1.4775
9
1.0937
1.1951
1.3048
1.4233
1.5513
10
1.1046
1.2190
1.3439
1.4802
1.6289
11
1.1157
1.2434
1.3842
1.5395
1.7103
12
1.1268
1.2684
1.4258
1.6010
1.7959
13
1.1381
1.2936
1.4685
1.6651
1.8856
14
1.1495
1.3195
1.5126
1.7317
1.9799
15
1.1610
1.3459
1.5580
1.8009
2.0789
16
1.1726
1.3728
1.6047
1.8730
2.1829
17
1.1843
3.4002
1.6528
1.9479
2.2920
18
1.1961
1.4282
1.7024
2.0258
2.4066
19
1.2081
1.4568
1.7535
2.1068
2.5270
20
1.2202
1.4859
1.8061
2.1911
2.6533
21
1.2324
1.5157
1.8603
2.2788
2.7860
22
1.2447
1.5460
1.9161
2.3699
2.9253
23
1.2572
1.5769
1.9735
2.4647
3.0715
24
1.2697
1.6084
2.0328
2.5633
3.2251
25
1.2824
1.6406
2.0938
2.6658
3.3864
26
1.2953
1.6734
2.1566
2.7725
3.5557
27
1.3082
1.7069
2.2213
2.8834
3.7335
28
1.3213
1.7410
2.2879
2.9987
3.9201
29
1.3345
1.7758
2.3566
3.1187
4.1161
30
1.3478
1.8114
2.4273
3.2434
4.3219
31
1.3613
1.8476
2.5001
3.3731
4.5380
32
1.3749
1.8845
2.5751
3.5081
4.7649
33
1.3887
1.9222
2.6523
3.6484
5.0032
34
1.4026
1.9607
2.7319
3.7943
5.2533
35
1.4166
1.9999
2.8139
3.9461
5.5160
36
1.4308
2.0399
2.8983
4.1039
5.7918
37
1.4451
2.0807
2.9852
4.2681
6.0814
38
1.4595
2.1223
3.0748
4.4388
6.3855
39
1.4741
2.1647
3.1670
4.6164
6.7048
40
1.4889
2.2080
3.2620
4.8010
7.0400
41
1.5038
2.2522
3.3599
4.9931
7.3920
42
1.5188
2.2972
3.4607
5.1928
7.7616
43
1.5340
2.3432
3.5645
5.4005
8.1500
44
1.5493
2.3901
3.6715
5.6165
8.5572
45
1.5648
2.4379
3.7816
5.8412
8.9850
46
1.5805
2.4866
3.8950
6.0748
9.4343
47
1.5963
2.5363
4.0119
6.3178
9.9060
48
1.6122
2.5871
4.1323
6.5705
10.4013
49
1.6283
2.6388
4.2562
6.8333
10.9213
50
1.6446
2.6916
4.3839
7.1067
11.4674
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%
1
1.0600
1.0700
1.0800
1.0900
1.1000
2
1.1236
1.1449
1.1664
1.1881
1.2100
3
1.1910
1.2250
1.2597
1.2950
1.3310
4
1.2625
1.3108
1.3605
1.4116
1.4641
5
1.3382
1.4026
1.4693
1.5386
1.6105
6
1.4185
1.5007
1.5869
1.6771
1.7716
7
1.5036
1.6058
1.7138
1.8280
1.9487
8
1.5938
1.7182
1.8509
1.9926
2.1436
9
1.6895
1.8385
1.9990
2.1719
2.3579
10
1.7908
1.9672
2.1589
2.3674
2.5937
11
1.8983
2.1049
2.3316
2.5804
2.8531
12
2.0122
2.2522
2.5182
2.8127
3.1384
13
2.1329
2.4098
2.7196
3.0658
3.4522
14
2.2609
2.5785
2.9372
3.3417
3.7975
15
2.3966
2.7590
3.1722
3.6425
4.1772
16
2.5404
2.9522
3.4259
3.9703
4.5950
17
2.6928
3.1588
3.7000
4.3276
5.0545
18
2.8543
3.3799
3.9960
4.7171
5.5599
19
3.0256
3.6165
4.3157
5.1417
6.1159
20
3.2071
3.8697
4.6610
5.6044
6.7275
21
3.3996
4.1406
5.0338
6.1088
7.4002
22
3.6035
4.4304
5.4365
6.6586
8.1403
23
3.8198
4.7405
5.8715
7.2579
8.9543
24
4.0489
5.0724
6.3412
7.9111
9.8497
25
4.2919
5.4274
6.8485
8.6231
10.8347
26
4.5494
5.8074
7.3964
9.3992
11.9182
27
4.8223
6.2139
7.9881
10.2451
13.1100
28
5.1117
6.6488
8.6271
11.1671
14.4210
29
5.4184
7.1143
9.3173
12.1722
15.8631
30
5.7435
7.6123
10.0627
13.2677
17.4494
31
6.0881
8.1451
10.8677
14.4618
19.1943
32
6.4534
8.7153
11.7371
15.7633
21.1138
33
6.8406
9.3253
12.6760
17.1820
23.2252
34
7.2510
9.9781
13.6901
18.7284
25.5477
35
7.6861
10.6766
14.7853
20.4140
28.1024
36
8.1473
11.4239
15.9682
22.2512
30.9127
37
8.6361
12.2236
17.2456
24.2538
34.0039
38
9.1543
13.0793
18.6253
26.4367
37.4043
39
9.7035
13.9948
20.1153
28.8160
41.1448
40
10.2857
14.9745
21.7245
31.4094
45.2593
41
10.9029
16.0227
23.4625
34.2363
49.7852
42
11.5570
17.1443
25.3395
37.3175
54.7637
43
12.2505
18.3444
27.3666
40.6761
60.2401
44
12.9855
19.6285
29.5560
44.3370
66.2641
45
13.7646
21.0025
31.9204
48.3273
72.8905
46
14.5905
22.4726
34.4741
52.6767
80.1795
47
15.4659
24.0457
37.2320
57.4176
88.1975
48
16.3939
25.7289
40.2106
62.5852
97.0172
49
17.3775
27.5299
43.4274
68.2179
106.7190
50
18.4202
29.4570
46.9016
74.3575
117.3909
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%
1
1.1100
1.1200
1.1300
1.1400
1.1500
2
1.2321
1.2544
1.2769
1.2996
1.3225
3
1.3676
1.4049
1.4429
1.4815
1.5209
4
1.5181
1.5735
1.6305
1.6890
1.7490
5
1.6851
1.7623
1.8424
1.9254
2.0114
6
1.8704
1.9738
2.0820
2.1950
2.3131
7
2.0762
2.2107
2.3526
2.5023
2.6600
8
2.3045
2.4760
2.6584
2.8526
3.0590
9
2.5580
2.7731
3.0040
3.2519
3.5179
10
2.8394
3.1058
3.3946
3.7072
4.0456
11
3.1518
3.4785
3.8359
4.2262
4.6524
12
3.4985
3.8960
4.3345
4.8179
5.3503
13
3.8833
4.3635
4.8980
5.4924
6.1528
14
4.3104
4.8871
5.5348
6.2613
7.0757
15
4.7846
5.4736
6.2543
7.1379
8.1371
16
5.3109
6.1304
7.0673
8.1372
9.3576
17
5.8951
6.8660
7.9861
9.2765
10.7613
18
6.5436
7.6900
9.0243
10.5752
12.3755
19
7.2633
8.6128
10.1974
12.0557
14.2318
20
8.0623
9.6463
11.5231
13.7435
16.3665
21
8.9492
10.8038
13.0211
15.6676
18.8215
22
9.9336
12.1003
14.7138
17.8610
21.6447
23
11.0263
13.5523
16.6266
20.3616
24.8915
24
12.2392
15.1786
18.7881
23.2122
28.6252
25
13.5855
17.0001
21.2305
26.4619
32.9190
26
15.0799
19.0401
23.9905
30.1666
37.8568
27
16.7386
21.3249
27.1093
34.3899
43.5353
28
18.5799
23.8839
30.6335
39.2045
50.0656
29
20.6237
26.7499
34.6158
44.6931
57.5755
30
22.8923
29.9599
39.1159
50.9502
66.2118
31
25.4104
33.5551
44.2010
58.0832
76.1435
32
28.2056
37.5817
49.9471
66.2148
87.5651
33
31.3082
42.0915
56.4402
75.4849
100.6998
34
34.7521
47.1425
63.7774
86.0528
115.8048
35
38.5749
52.7996
72.0685
98.1002
133.1755
36
42.8181
59.1356
81.4374
111.8342
153.1519
37
47.5281
66.2318
92.0243
127.4910
176.1246
38
52.7562
74.1797
103.9874
145.3397
202.5433
39
58.5593
83.0812
117.5058
165.6873
232.9248
40
65.0009
93.0510
132.7816
188.8835
267.8635
41
72.1510
104.2171
150.0432
215.3272
308.0431
42
80.0876
116.2314
169.5488
245.4730
354.2495
43
88.8972
130.7299
191.5901
279.8392
407.3870
44
98.6759
146.4175
216.4968
319.0167
468.4950
45
109.5302
163.9876
244.6414
363.6791
538.7693
46
121.5786
183.6661
276.4448
414.5941
619.5847
47
134.9522
205.7061
312.3826
472.6373
712.5224
48
149.7970
230.3908
352.9923
538.8065
819.4007
49
166.2746
258.0377
398.8813
614.2395
942.3108
50
184.5648
289.0022
450.7359
700.2330
1,083.6574
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%
1
1.1600
1.1700
1.1800
1.1900
1.2000
2
1.3456
1.3689
1.3924
1.4161
1.4400
3
1.5609
1.6016
1.6430
1.6852
1.7280
4
1.8106
1.8739
1.9388
2.0053
2.0736
5
2.1003
2.1924
2.2878
2.3864
2.4883
6
2.4364
2.5652
2.6996
2.8398
2.9860
7
2.8262
3.0012
3.1855
3.3793
3.5832
8
3.2784
3.5115
3.7589
4.0214
4.2998
9
3.8030
4.1084
4.4355
4.7854
5.1598
10
4.4114
4.8068
5.2338
5.6947
6.1917
11
5.1173
5.6240
6.1759
6.7767
7.4301
12
5.9360
6.5801
7.2876
8.0642
8.9161
13
6.8858
7.6987
8.5994
9.5964
10.6993
14
7.9875
9.0075
10.1472
11.4198
12.8392
15
9.2655
10.5387
11.9737
13.5895
15.4070
16
10.7480
12.3303
14.1290
16.1715
18.4884
17
12.4677
14.4265
16.6722
19.2441
22.1861
18
14.4625
16.8790
19.6733
22.9005
26.6233
19
16.7765
19.7484
23.2144
27.2516
31.9480
20
19.4608
23.1056
27.3930
32.4294
38.3376
21
22.5745
27.0336
32.3238
38.5910
46.0051
22
26.1864
31.6293
38.1421
45.9233
55.2061
23
30.3762
37.0062
45.0076
54.6487
66.2474
24
35.2364
43.2973
53.1090
65.0320
79.4968
25
40.8742
50.6578
62.6686
77.3881
95.3962
26
47.4141
59.2697
73.9490
92.0918
114.4755
27
55.0004
69.3455
87.2598
109.5893
137.3706
28
63.8004
81.1342
102.9666
130.4112
164.8447
29
74.0085
94.9271
121.5005
155.1893
197.8136
30
85.8499
111.0647
143.3706
184.6753
237.3763
31
99.5859
129.9456
169.1774
219.7636
284.8516
32
115.5196
152.0364
199.6293
261.5187
341.8219
33
134.0027
177.8826
235.5625
311.2073
410.1863
34
155.4432
208.1226
277.9638
370.3366
492.2235
35
180.3141
243.5035
327.9973
440.7006
590.6682
36
209.1643
284.8991
387.0368
524.4337
708.8019
37
242.6306
333.3319
456.7034
624.0761
850.5623
38
281.4515
389.9983
538.9100
742.6506
1,020.6747
39
326.4838
456.2980
635.9139
883.7542
1,224.8096
40
378.7212
533.8687
750.3783
1,051.6675
1,469.7716
41
439.3165
624.6264
885.4464
1,251.4843
1,763.7259
42
509.6072
730.8129
1,044.8268
1,489.2664
2,116.4711
43
591.1443
855.0511
1,232.8956
1,772.2270
2,539.7653
44
685.7274
1,000.4098
1,454.8168
2,108.9501
3,047.7183
45
795.4438
1,170.4794
1,716.6839
2,509.6506
3,657.2620
46
922.7148
1,369.4609
2,025.6870
2,986.4842
4,388.7144
47
1,070.3492
1,602.2692
2,390.3106
3,553.9162
5,266.4573
48
1,241.6051
1,874.6550
2,820.5665
4,229.1603
6,319.7487
49
1,440.2619
2,193.3464
3,328.2685
5,032.7008
7,583.6985
50
1,670.7038
2,566.2153
3,927.3569
5,988.9139
9,100.4182
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%
1
1.2100
1.2200
1.2300
1.2400
1.2500
2
1.4641
1.4884
1.5129
1.5376
1.5625
3
1.7716
1.8158
1.8609
1.9066
1.9531
4
2.1436
2.2153
2.2889
2.3642
2.4414
5
2.5937
2.7027
2.8153
2.9316
3.0518
6
3.1384
3.2973
3.4628
3.6352
3.8147
7
3.7975
4.0227
4.2593
4.5077
4.7684
8
4.5950
4.9077
5.2389
5.5895
5.9605
9
5.5599
5.9874
6.4439
6.9310
7.4506
10
6.7275
7.3046
7.9259
8.5944
9.3132
11
8.1403
8.9117
9.7489
10.6571
11.6415
12
9.8497
10.8722
11.9912
13.2148
14.5519
13
11.9182
13.2641
14.7491
16.3863
18.1899
14
14.4210
16.1822
18.1414
20.3191
22.7374
15
17.4494
19.7423
22.3140
25.1956
28.4217
16
21.1138
24.0856
27.4462
31.2426
35.5271
17
25.5477
29.3844
33.7588
38.7408
44.4089
18
30.9127
35.8490
41.5233
48.0386
55.5112
19
37.4043
43.7358
51.0737
59.5679
69.3889
20
45.2593
53.3576
62.8206
73.8641
86.7362
21
54.7637
65.0963
77.2694
91.5915
108.4202
22
66.2641
79.4175
95.0413
113.5735
135.5253
23
80.1795
96.8893
116.9008
140.8312
169.4066
24
97.0172
118.2050
143.7880
174.6306
211.7582
25
117.3909
144.2101
176.8593
216.5420
264.6978
26
142.0429
175.9364
217.5369
268.5121
330.8722
27
171.8719
214.6424
267.5704
332.9550
413.5903
28
207.9651
261.8637
329.1115
412.8642
516.9879
29
251.6377
319.4737
404.8072
511.9516
646.2349
30
304.4816
389.7579
497.9129
634.8199
807.7936
31
368.4228
475.5046
612.4328
787.1767
1,009.7420
32
445.7916
580.1156
753.2924
976.0991
1,262.1774
33
539.4078
707.7411
926.5496
1,210.3629
1,577.7218
34
652.6834
863.4441
1,139.6560
1,500.8500
1,972.1523
35
789.7470
1,053.4018
1,401.7769
1,861.0540
2,465.1903
36
955.5938
1,285.1502
1,724.1856
2,307.7070
3,081.4879
37
1,156.2685
1,567.8833
2,120.7483
2,861.5567
3,851.8599
38
1,399.0849
1,912.8176
2,608.5204
3,548.3303
4,814.8249
39
1,692.8927
2,333.6375
3,208.4801
4,399.9295
6,018.5311
40
2,048.4002
2,847.0378
3,946.4305
5,455.9126
7,523.1638
41
2,478.5643
3,473.3861
4,854.1095
6,765.3317
9,403.9548
42
2,999.0628
4,237.5310
5,970.5547
8,389.0113
11,754.9435
43
3,628.8659
5,169.7878
7,343.7823
10,402.3740
14,693.6794
44
4,390.9278
6,307.1411
9,032.8522
12,898.9437
18,367.0992
45
5,313.0226
7,694.7122
11,110.4082
15,994.6902
22,958.8740
46
6,428.7574
9,387.5489
13,665.8021
19,833.4158
28,698.5926
47
7,778.7964
11,452.8096
16,808.9365
24,593.4356
35,873.2407
48
9,412.3437
13,972.4277
20,674.9920
30,495.8602
44,841.5509
49
11,388.9358
17,046.3619
25,430.2401
37,814.8666
56,051.9386
50
13,780.6123
20,796.5615
31,279.1953
46,890.4346
70,064.9232
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%
1
1.2600
1.2700
1.2800
1.2900
1.3000
2
1.5876
1.6129
1.6834
1.6641
1.6900
3
2.0004
2.0484
2.0972
2.1467
2.1970
4
2.5205
2.6014
2.6844
2.7692
2.8561
5
3.1758
3.3038
3.4360
3.5723
3.7129
6
4.0015
4.1959
4.3980
4.6083
4.8268
7
5.0419
5.3288
5.6295
5.9447
6.2749
8
6.3528
6.7675
7.2058
7.6686
8.1573
9
8.0045
8.5947
9.2234
9.8925
10.6045
10
10.0857
10.9153
11.8059
12.7614
13.7858
11
12.7080
13.8625
15.1116
16.4622
17.9216
12
16.0120
17.6053
19.3428
21.2362
23.2981
13
20.1752
22.3588
24.7588
27.3947
30.2875
14
25.4207
28.3957
31.6913
35.3391
39.3738
15
32.0301
36.0625
40.5648
45.5875
51.1859
16
40.3579
45.7994
51.9230
58.8079
66.5417
17
50.8510
58.1652
66.4614
75.8621
86.5042
18
64.0722
73.8698
85.0706
97.8622
112.4554
19
80.7310
93.8147
108.8904
126.2422
146.1920
20
101.7211
119.1446
139.3797
162.8524
190.0496
21
128.1685
151.3137
178.4060
210.0796
247.0645
22
161.4624
192.1683
228.3596
271.0027
321.1839
23
203.4804
244.0538
292.3003
349.5935
417.5391
24
256.3853
309.0483
374.1444
450.9756
542.8008
25
323.0454
393.6344
478.9049
581.7585
705.6410
26
407.0373
499.9157
612.9982
750.4685
917.3333
27
512.8670
634.8929
784.6377
968.1044
1,192.5333
28
646.2124
806.3140
1,004.3363
1,248.8546
1,550.2933
29
814.2276
1,024.0187
1,285.5504
1,611.0225
2,015.3813
30
1,025.9267
1,300.5038
1,645.5046
2,078.2190
2,619.9956
31
1,292.6677
1,651.6398
2,106.2458
2,680.9025
3,405.9943
32
1,628.7613
2,097.5826
2,695.9947
3,458.3642
4,427.7926
33
2,052.2392
2,663.9299
3,450.8732
4,461.2898
5,756.1304
34
2,585.8215
3,383.1910
4,417.1177
5,755.0639
7,482.9696
35
3,258.1350
4,296.6525
5,653.9106
7,424.0324
9,727.8604
36
4,105.2501
5,456.7487
7,237.0056
9,577.0018
12,646.2186
37
5,172.6152
6,930.0709
9,263.3671
12,354.3324
16,440.0841
38
6,517.4951
8,801.1900
11,857.1099
15,937.0888
21,372.1094
39
8,212.0438
11,177.5113
15,177.1007
20,558.8445
27,783.7422
40
10,347.1753
14,195.4393
19,426.6889
26,520.9094
36,118.8648
41
13,037.4408
18,028.2080
24,866.1618
34,211.9731
46,954.5243
42
16,427.1754
22,895.8241
31,828.6871
44,133.4453
61,040.8815
43
20,698.2410
29,077.6966
40,740.7195
56,932.1445
79,353.1460
44
26,079.7837
36928.6747
52,148.1210
73,442.4664
103,159.0898
45
32,860.5275
46,899.4169
66,749.5949
94,740.7816
134,106.8167
46
41,404.2646
59,562.2594
85,439.4814
122,215.6083
174,338.8617
47
52,169.3734
75,644.0695
109,362.5362
157,658.1347
226,640.5202
48
65,733.4105
96,067.9683
139,984.0464
203,378.9938
294,632.6763
49
82,824.0972
122,006.3197
179,179.5794
262,358.9020
383,022.4792
50
104,358.3625
154,948.0260
229,349.8616
338,442.9836
497,929.2230
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%
1
1.3100
1.3200
1.3300
1.3400
1.3500
2
1.7161
1.7424
1.7689
1.7956
1.8225
3
2.2481
2.2999
2.3526
2.4061
2.4604
4
2.9450
3.0360
3.1290
3.2242
3.3215
5
3.8579
4.0075
4.1616
4.3204
4.4840
6
5.0539
5.2899
5.5349
5.7893
6.0534
7
6.6206
6.9826
7.3614
7.7577
8.1722
8
8.6730
9.2170
9.7907
10.3953
11.0324
9
11.3617
12.1665
13.0216
13.9297
14.8937
10
14.8838
16.0598
17.3187
18.6659
20.1066
11
19.4977
21.1989
23.0339
25.0113
27.1439
12
25.5420
27.9825
30.6351
33.5164
36.6442
13
33.4601
36.9370
40.7447
44.9120
49.4697
14
43.8327
48.7568
54.1905
60.1821
66.7841
15
57.4208
64.3590
72.0733
80.6440
90.1585
16
75.2213
84.9538
95.8575
108.0629
121.7139
17
98.5399
112.1390
127.4905
144.8043
164.3138
18
129.0872
148.0235
169.5624
194.0378
221.8236
19
169.1043
195.3911
225.5180
260.0107
299.4619
20
221.5266
257.9162
299.9389
348.4143
404.2736
21
290.1999
340.4494
398.9188
466.8752
545.7693
22
380.1618
449.3932
530.5620
625.6127
736.7886
23
498.0120
593.1990
705.6474
838.3210
994.6646
24
652.3957
783.0227
938.5110
1,123.3502
1,342.7973
25
854.6384
1,033.5900
1,248.2197
1,505.2892
1,812.7763
26
1,119.5763
1,364.3387
1,660.1322
2,017.0876
2,447.2480
27
1,466.6449
1,800.9271
2,207.9758
2,702.8974
3,303.7848
28
1,921.3048
2,377.2238
2,936.6078
3,621.8825
4,460.1095
29
2,516.9093
3,137.9354
3,905.6884
4,853.3225
6,021.1478
30
3,297.1512
4,142.0748
5,194.5655
6,503.4522
8,128.5495
31
4,319.2681
5,467.5387
6,908.7722
8,714.6259
10,973.5418
32
5,658.2413
7,217.1511
9,188.6670
11,677.5987
14,814.2815
33
7,412.2960
9,526.6395
12,220.9271
15,647.9823
19,999.2800
34
9,710.1078
12,575.1641
16,253.8330
20,968.2963
26,999.0280
35
12,720.2412
16,599.2166
21,617.5979
28,097.5170
36,448.6878
36
16,663.5160
21,910.9659
28,751.4052
37,650.6728
49,205.7285
37
21,829.2060
28,922.4750
38,239.3689
50,451.9015
66,427.7335
38
28,596.2599
38,177.6670
50,858.3606
67,705.5481
89,677.4402
39
37,461.1004
50,394.5205
67,641.6196
90,591.4344
121,064.5442
40
49,074.0415
66,520.7670
89,963.3541
121,392.5221
163,437.1347
41
64,286.9944
87,807.4125
119,651.2609
162,665.9796
220,640.1318
42
84,215.9627
115,905.7845
159,136.1770
217,972.4127
297,864.1780
43
110,322.9111
152,995.6355
211,651.1154
292,083.0330
402,116.6402
44
144,523.0136
201,954.2388
281,495.9835
391,391.2642
542,857.4643
45
189,325.1478
266,579.5953
374,389.6581
524,464.2940
732,857.5768
46
248,015.9436
351,885.0658
497,938.2452
702,782.1540
989,357.7287
47
324,900.8861
464,488.2868
662,257.8662
941,728.0864
1,335,632.9338
48
425,620.1608
614,124.5386
880,802.9620
1,261,915.6358
1,803,104.4606
49
557,562.4107
809,324.3909
1,171,467.9394
1,690,966.9519
2,434,191.0218
50
730,406.7580
1,068,308.1960
1,558,052.3594
2,265,895.7156
3,286,157.8794
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%
1
1.3600
1.3700
1.3800
1.3900
1.4000
2
1.8496
1.8769
1.9044
1.9321
1.9600
3
2.5155
2.5714
2.6281
2.6856
2.7440
4
3.4210
3.5228
3.6267
3.7330
3.8416
5
4.6526
4.8262
5.0049
5.1889
5.3782
6
6.3275
6.6119
6.9068
7.2125
7.5295
7
8.6054
9.0582
9.5313
10.0254
10.5414
8
11.7034
12.4098
13.1532
13.9354
14.7579
9
15.9166
17.0014
18.1515
19.3702
20.6610
10
21.6466
23.2919
25.0490
26.9245
28.9255
11
29.4393
31.9100
34.5677
37.4251
40.4957
12
40.0375
43.7166
47.7034
52.0209
56.6939
13
54.4510
59.8918
65.8306
72.3090
79.3915
14
74.0535
82.0517
90.8463
100.5095
111.1201
15
100.7126
112.4109
125.3679
139.7082
155.5681
16
136.9691
154.0030
173.0077
194.1944
217.7953
17
186.2779
210.9841
238.7506
269.9303
304.9135
18
253.3380
289.0482
329.4758
375.2031
426.8789
19
344.5396
395.9960
454.6766
521.5323
597.6304
20
468.5740
542.5145
627.4538
724.9299
836.6826
21
637.2606
743.2449
865.8862
1,007.6525
1,171.3556
22
866.6744
1,018.2454
1,194.9229
1,400.6370
1,639.8978
23
1,178.6772
1,394.9963
1,648.9937
1,946.8855
2,295.8569
24
1,603.0010
1,911.1449
2,275.6113
2,706.1708
3,214.1997
25
2,180.0813
2,618.2685
3,761.5774
3,761.5774
4,499.7958
26
2,964.9107
3,587.0278
4,333.6741
5,228.5926
6,299.8314
27
4,032.2786
4,914.2281
5,980.4702
7,267.7438
8,819.7640
28
5,483.8988
6,732.4925
8,253.0489
10,102.1638
12,347.6696
29
7,458.1024
9,223.5150
11,389.2075
14,042.0077
17,286.7374
30
10,143.0192
12,636.2153
·15,717.1064
19,518.3907
24,201.4323
31
13,794.5062
17,311.6149
21,689.6068
27,130.5631
33,882.0053
32
18,760.5285
23,716.9124
29,931.6574
37,711.4827
47,434.8074
33
25,514.3187
32,492.1700
41,305.6871
52,418.9610
66,408.7304
34
34,699.4735
44,514.2728
57,001.8483
72,862.3558
92,972.2226
35
47,191.2839
60,984.5538
78,662.5506
101,278.6745
130,161.1116
36
64,180.1461
83,548.8387
108,554.3198
140,777.3576
182,225.5562
37
87,284.9987
114,461.9090
149,804.9613
195,680.5270
255,115.7786
38
118,707.5982
156,812.8153
206,730.8466
271,995.9326
357,162.0901
39
161,442.3336
214,833.5570
285,288.5684
378,074.3463
500,026.9261
40
219,561.5736
294,321.9731
393,698.2244
525,523.3413
700,037.6966
41
298,603.7402
403,221.1031
543,303.5496
730,477.4445
980,052.7752
42
406,101,0866
552,412.9113
749,758.8985
1,015,363.6478
1,372,073.8853
43
552,297.4778
756,805.6884
1,034,667.2800
1,411,355.4704
1,920,903.4394
44
751,124.5698
1,036,823.7932
1,427,840.8462
1,961,784.1039
2,689,264.8152
45
1,029,529.4149
1,420,448.5966
1,970,420.3678
2,726,879.9044
3,764,970.7413
46
1,389,280.0043
1,946,014.5774
2,719,180.1075
3,790,363.0672
5,270,959.0378
47
1,889,420.8509
2,666,039.9710
3,752,468.5484
5,268,604.6634
7,379,342.6530
48
2,569,612.2960
3,652,474.7603
5,178,406.5968
7,323,360.4821
10,331,079.7142
49
3,494,672.7225
5,003,890.4215
7,146,201.1035
10,179,471.0701
14,463,511.5998
50
4,752,754.9027
6,855,329.8775
9,861,757.5229
14,149,464.7874
20,248,916.239
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%
1
1.4100
1.4200
1.4300
1.4400
1.4500
2
1.9881
2.0164
2.0449
2.0736
2.1025
3
2.8032
2.8633
2.9242
2.9860
3.0486
4
3.9525
4.0659
4.1816
4.2998
4.4205
5
5.5731
5.7735
5.9797
6.1917
6.4097
6
7.8580
8.1984
8.5510
8.9161
9.2941
7
11.0798
8.5510
12.2279
12.8392
13.4765
8
15.6226
16.5313
17.4859
18.4884
19.5409
9
22.0278
23.4744
25.0049
26.6233
28.3342
10
31.0593
33.3337
35.7569
38.3376
41.0847
11
43.7396
47.3338
51.1324
55.2061
59.5728
12
61.7489
67.2141
73.1194
79.4968
86.3806
13
87.0660
95.4440
104.5607
114.4755
125.2518
14
122.7630
135.5304
149.5218
164.8447
181.6151
15
173.0959
192.4532
213.8162
237.3763
263.3419
16
244.0652
273.2836
305.7571
341.8219
381.8458
17
344.1319
388.0627
437.2327
492.2235
553.6764
18
485.2260
551.0490
625.2428
708.8019
802.8308
19
684.1686
782.4895
894.0972
1,020.6747
1,164.1047
20
964.6777
1,111.1351
1,278.5589
1,469.7716
1,687.9518
21
1,360.1956
1,577.8119
1,828.3393
2,116.4711
2,447.5301
22
1,917.8758
2,240.4929
2,614.5252
3,047.7183
3,548.9187
23
2,704.2049
3,181.5000
3,738.7710
4,388.7144
5,145.9321
24
3,812.9289
4,517.7299
5,346.4425
6,319.7847
7,461.6015
25
5,376.2297
6,415.1765
7,645.4128
9,100.4382
10,819.3222
26
7,580.4839
9,109.5506
10,932.9402
13,104.6309
15,688.0173
27
10,688.4823
12,935.5619
15,634.1045
18,870.6686
22,747.6250
28
15,070.7600
18,368.4979
22,356.7695
27,173.7627
32,984.0563
29
21,249.7716
26,083.2670
31,970.1804
39,130.2183
47,826.8816
30
29,962.1780
37,038.2392
45,717.3579
56,347.5144
69,348.9783
31
42,246.6710
52,594.2996
65,375.8218
81,140.4207
100,556.0185
32
59,567.8061
74,683.9054
93,487.4252
116,842.2058
145,806.2269
33
83,990.6066
106,051.1457
133,687.0181
168,252.7762
211,419.0289
34
118,426.7552
150,592.6269
191,172.4358
242,283.9979
306,557.5920
35
166,981.7249
213,841.5302
273,376.5833
348,888.9569
444,508.5083
36
235,444.2321
303,654.9728
390,928.5141
502,400.0980
644,537.3371
37
331,976.3673
431,190.0614
559,027.7751
723,456.1411
934,579.1388
38
468,086.6778
612,289.8872
799,409.7184
1,041,776.8432
1,355,139.7513
39
660,002.2158
869,451.6399
1,143,155.8973
1,500,158.6542
1,964,952.6393
40
930,603.1242
1,234,621.3286
1,634,712.9332
2,160,228.4620
2,849,181.3270
41
1,312,150.4052
1,753,162.2866
2,337,639.4945
3,110,728.9853
4,131,312.9242
42
1,850,132.0713
2,489,490.4470
3,342,824.4771
4,479,449.7388
5,990,403.7400
43
2,608,686.2205
3,535,076.4348
4,780,239.0022
6,450,407.6239
8,686,085.4230
44
3,678,247.5709
5,019,808.5374
6,835,741.7732
9,288,586.9784
12,594,823.8634
45
5,186,329.0750
7,128,128.1231
9,775,110.7357
13,375,565.2489
18,262,494.6019
46
7,312,623.9957
10,121,941.9348
13,978,408.3520
19,260,813.9585
26,480,617.1729
47
10,310,940.8339
14,373,157.5474
19,989,123.9434
27,735,572.1001
38,396,894.9007
48
14,538,426.5758
20,409,883.7173
28,584,447.2390
39,939,223.8242
55,675,497.6060
49
20,499,181.4719
28,982,034.8786
40,875,759.5516
57,512,482.3069
80,729,471.5287
50
28,903,845.8754
41,154,489.5276
58,452,336.1591
82,817,974.5219
117,057,733.7166
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%
1
1.4600
1.4700
1.4800
1.4900
1.5000
2
2.1316
2.1609
2.1904
2.2201
2.2500
3
3.1121
3.1765
3.2418
3.3079
3.3750
4
4.5437
4.6695
4.7979
4.9288
5.5625
5
6.6338
6.8641
7.1008
7.3440
7.5938
6
9.6854
10.0903
10.5092
10.9425
11.3906
7
14.1407
14.8327
15.5537
16.3044
17.0859
8
20.6454
21.8041
23.0194
24.2935
25.6289
9
30.1423
32.0521
34.0687
36.1973
38.4434
10
44.0077
47.1165
50.4217
53.9340
57.6650
11
64.2512
69.2613
74.6241
80.3617
86.4976
12
93.8068
101.8141
110.4436
119.7389
129.7463
13
136.9579
149.6668
163.4565
178.4109
194.6195
14
199.9586
220.0101
241.9157
265.8323
291.9293
15
291.9395
323.4149
358.0352
396.0901
437.8939
16
426.2316
475.4199
529.8921
590.1743
656.8408
17
622.2982
698.8673
784.2403
879.3597
985.2613
18
908.5554
1,027.3349
1,160.6757
1,310.2460
1,477.8919
19
1,326.4909
1,510.1822
1,717.8000
1,952.2665
2,216.8378
20
1,936.6766
2,219.9679
2,542.3440
2,908.8771
3,325.2567
21
2,824.5479
3,263.3528
3,762.6691
4,334.2268
4,987.8850
22
4,128.2199
4,797.1286
5,568.7502
6,457.9980
7,481.8276
23
6,027.2011
7,051.7791
8,241.7503
9,622.4170
11,222.7415
24
8,799.7136
10,366.1153
12,197.7905
14,337.4013
16,834.1122
25
12,847.5819
15,238.1895
18,052.7299
21,362.7280
25,251.1683
26
18,757.4696
22,400.1385
26,718.0403
31,830.4647
37,876.7524
27
27,385.9056
32,928.2386
39,542.6996
47,427.3924
56,815.1287
28
39,983.4221
48,404.4593
58,523.1954
70,666.8146
85,222.6930
29
58,375.7963
71,154.5551
86,614.3292
105,293.5538
127,834.0395
30
85,228.6626
104,597.1960
128,189.2073
156,887.3952
191,751.0592
31
124,433.8474
153,757.8782
189,720.0268
233,762.2188
287,626.5888
32
181,673.4172
226,024.0809
280,785.6396
348,305.7060
431,439.8833
33
265,243.1891
332,255.3989
415,562.7466
518,975.5019
647,159.8249
34
387,255.0561
488,415.4364
615,032.8650
773,273.4979
970,739.7374
35
565,382.3818
717,970.6916
910,248.6402
1,152,177.5118
1,456,109.6060
36
825,472.8775
1,055,416.9166
1,347,167.9875
1,716,744.4926
2,184,164.4091
37
1,205,190.4011
1,551,462.8674
1,993,808.6215
2,557,949.2940
3,276,246.6136
38
1,759,577.9856
2,280,650.4151
2,950,836.7598
3,811,344.4481
4,914,369.9204
39
2,568,983.8590
3,352,556.1102
4,367,238.4045
5,678,903.2277
7,371,554.8806
40
3,750,716.4342
4,928,257.4821
6,463,512.8387
8,461,565.8093
11,057,332.3209
41
5,476,045.9939
7,244,538.4986
9,565,999.0012
12,607,733.0558
16,585,998.4814
42
7,995,027.1511
10,649,471.5930
14,157,678.5218
18,785,522.2531
24,878,997.7221
43
11,672,739.6405
15,654,723.2417
20,953,364.2123
27,990,428.1572
37,318,496.5832
44
17,042,199.8752
23,012,443.1652
31,010,979.0342
41,705,737.9542
55,977,744.8747
45
24,881,611.8177
33,828,291.4529
45,896,248.9706
62,141,549.5517
83,966,617.3121
46
36,327,153.2539
49,727,588.4357
67,926,448.4765
92,590,908.8321
125,949,925.9681
47
53,037,643.7507
73,099,555.0007
100,531,143.7453
137,960,454.1598
188,924,888.9522
48
77,434,959.8762
107,456,345.8511
148,786,092.7430
205,561,076.6982
283,387,333.4283
49
113,055,041.4189
157,960,828.4011
220,203,417.2597
306,286,004.2803
425,081,000.1424
50
165,060,360.4716
232,202,417.7496
325,901,057.5443
456,050,366.3776
637,621,500.2135

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

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：
則老張期望的年化收益率應該不低於：
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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