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

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

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

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

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

（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

（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

（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

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

=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

=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

=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

=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

=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

=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

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

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

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。