年金現值

年金現值就是在已知等額收付款金額未來本利(Future Value)、利率(interest)（這裡我們默認為年利率）和計息期數n時，考慮貨幣時間價值，計算出的這些收付款到現在的等價票面金額Present Value。 年金分為：普通年金（後付年金）、先付年金、遞延年金、永續年金等幾種。對應的，年金現值也可分為：普通年金現值、先付年金現值、遞延年金現值、永續年金現值。

基本信息

• 中文名：年金現值
• 英文名：Present Value of Annuity

• 類別：會計學
• 種類：普通年金現值、先付年金現值
• 種類2：遞延年金現值、永續年金現值

分類

年金（Annuity）是指一定期間內每期等額收付的款項。 因此，可以說年金是複利的產物，是複利的一種特殊形式（等額收付）

普通年金（Ordinary Annuity）是指 每期 期末收付款項的年金 ，例如採用直線法計提的單項固定資產的折舊（折舊總額會隨著固定資產數量的變化而變化，不是年金，但就單項固定資產而言，其使用期內按直線法計提的折舊額是一定的）、一定期間的租金（租金不變期間）、每年員工的社會保險金（按月計算，每年7月1日到次年6月30日不變）、一定期間的貸款利息（即銀行存貸款利率不變且存貸金額不變期間，如貸款金額在銀行貸款利率不變期間有變化可以視為多筆年金）等。

先付年金（Annuity Due）是指 每期 期初收付款項的年金 ，例如先付錢後用餐的餐廳，每一道菜（包括米飯、面、餃子和餛飩等）分別出來之後都是先付年金。

遞延年金（Deferred Annuity）是指在 預備計算時 尚未發生收付，但 未來 一定會發生若干期等額收付的年金 ，一般是在金融理財和社保回饋方面會產生遞延年金。遞延年金在做投資或其他資本預算時具有相當可觀的作用。

永續年金（Perpetual Annuity）即 無限期連續收付款的年金 ，最典型的就是諾貝爾獎金。

計算

普通年金現值

普通年金現值是以計算期期末為基準，在給定投資報酬率下按照貨幣時間價值計算出的未來一段期間內每年或每月收取或給付的年金現金流的折現值之和。類似普通年金終值，計算普通年金現值時，同樣要考慮到現金流是期初年金還是期末年金。

例如：某公司租用某設備，每年年末需要支付租金100元，年利率為10%，問5年內應支付的租金總額的現值是多少?

年金現值

公式推導如下：

年金現值

年金現值

年金現值

兩邊同時乘以 得

年金現值

兩式作差得

最後兩邊同時除以i得到公式。

如果年金的期數n很多，用上述方法計算現值顯然相當繁瑣。由於每年支付額相等，折算現值的係數又是有規律的，所以，可找出簡便的計算方法。

設每年的收付金額為A，利率為i，期數為n，則按複利計算的年金現值P為：

年金現值

。

年金現值

式中， 稱為“年金現值係數”，記作（P/A，i，n），可查普通年金現值係數表。

先付年金現值

先付年金現值： 是其最後一期期末時的本利和，相當於各期期初等額收付款項的複利現值之和。

n期先付年金與n期普通年金的收付款次數相同，但由於付款時間不同，n期先付年金現值比n期普通年金的現值多計算一期利息。因此在n期普通年金現值的基礎上乘以（1+i）而將分母加1就得出n期先付年金的現值了，公式為：

記作P(A，i，n)=A·[(P/A，i，n-1)+1]

則如果上例為每年初計息的話，經過5年，逐年的現值為年金現值， 計算為：

年金現值

遞延年金現值

遞延年金終值，它的計算完全可以利用普通年金終值公式來計算（因為遞延期內沒有年金）

永續年金現值

年金現值

永續年金因為是無限期收付的，所以其計算公式反而簡單，是

年金現值

也就是說，如果這筆十萬美元投資是一筆專項基金的話，其永續現值為 （美元）

係數表

1%~5%

年金現值係數表　

利率 —— 期間	1%	2%	3%	4%	5%
1	0.9901	0.9804	0.9709	0.9615	0.9524
2	1.9704	1.9416	1.9135	1.8861	1.8594
3	2.9410	2.8839	2.8286	2.7751	2.7232
4	3.9020	3.8077	3.7171	3.6299	3.5460
5	4.8534	4.7135	4.5797	4.4518	4.3295
6	5.7955	5.6014	5.4172	5.2421	5.0757
7	6.7282	6.4720	6.2303	6.0021	5.7864
8	7.6517	7.3255	7.0197	6.7327	6.4632
9	8.5660	8.1622	7.7861	7.4353	7.1078
10	9.4713	8.9826	8.5302	8.1109	7.7217
11	10.3676	9.7868	9.2526	8.7605	8.3064
12	11.2551	10.5753	9.9540	9.3851	8.8633
13	12.1337	11.3484	10.6350	9.9856	9.3936
14	13.0037	12.1062	11.2961	10.5631	9.8986
15	13.8651	12.8493	11.9379	11.1184	10.3797
16	14.7179	13.5777	12.5611	11.6523	10.8378
17	15.5623	14.2919	13.1661	12.1657	11.2740
18	16.3983	14.9920	13.7535	12.6593	11.6896
19	17.2260	15.6785	14.3238	13.1340	12.0853
20	18.0456	16.3514	14.8775	13.5903	12.4622
21	18.8570	17.0112	15.4150	14.0292	12.8212
22	19.6604	17.6580	15.9369	14.4511	13.1630
23	20.4558	18.2922	16.4436	14.8568	13.4886
24	21.2434	18.9139	16.9355	15.2470	13.7986
25	22.0232	19.5235	17.4131	15.6221	14.0939
26	22.7952	20.1210	17.8768	15.9828	14.3752
27	23.5596	20.7069	18.3270	16.3296	14.6430
28	24.3164	21.2813	18.7641	16.6631	14.8981
29	25.0658	21.8444	19.1885	16.9837	15.1411
30	25.8077	22.3965	19.6004	17.2920	15.3725
31	26.5423	22.9377	20.0004	17.5885	15.5928
32	27.2696	23.4683	20.3888	17.8736	15.8027
33	27.9897	23.9886	20.7658	18.1476	16.0025
34	28.7027	24.4986	21.1318	18.4112	16.1929
35	29.4086	24.9986	21.4872	18.6646	16.3742
36	30.1076	25.4888	21.8323	18.9083	16.5469
37	30.7995	25.9695	22.1672	19.1426	16.7113
38	31.4847	26.4406	22.4925	19.3679	16.8679
39	32.1630	26.9026	22.8082	19.5845	17.0170
40	32.8347	27.3555	23.1148	19.7928	17.1591
41	33.4997	27.7995	23.4124	19.9931	17.2944
42	34.1581	28.2348	23.7014	20.1856	17.4232
43	34.8100	28.6616	23.9819	20.3708	17.5459
44	35.4555	29.0800	24.2543	20.5488	17.6628
45	36.0945	29.4902	24.5187	20.7200	17.7741
46	36.7272	29.8923	24.7754	20.8847	17.8801
47	37.3537	30.2866	25.0247	21.0429	17.9810
48	37.9740	30.6731	25.2667	21.1951	18.0772
49	38.5881	31.0521	25.5017	21.3414	18.1687
50	39.1961	31.4236	25.7298	21.4822	18.2559

6%~10%

年金現值係數表

利率 —— 期數	6%	7%	8%	9%	10%
1	0.9434	0.9346	0.9259	0.9174	0.9091
2	1.8334	1.8080	1.7833	1.7591	1.7355
3	2.6730	2.6243	2.5771	2.5313	2.4869
4	3.4651	3.3872	3.3121	3.2397	3.1699
5	4.2124	4.1002	3.9927	3.8897	3.7908
6	4.9173	4.7665	4.6228	4.4859	4.3553
7	5.5824	5.3893	5.2064	5.0330	4.8684
8	6.2098	5.9713	5.7466	5.5348	5.3349
9	6.8017	6.5152	6.2469	5.9952	5.7590
10	7.3601	7.0236	6.7101	6.4176	6.1446
11	7.8869	7.4987	7.1390	6.8052	6.4951
12	8.3838	7.9427	7.5361	7.1607	6.8137
13	8.8527	8.3577	7.9038	7.4869	7.1034
14	9.2950	8.7455	8.2442	7.7862	7.3667
15	9.7122	9.1079	8.5595	8.0607	7.6061
16	10.1059	9.4466	8.8514	8.3126	7.8237
17	10.4773	9.7632	9.1216	8.5436	8.0216
18	10.8276	10.0591	9.3719	8.7556	8.2014
19	11.1581	10.3356	9.6036	8.9501	8.3649
20	11.4699	10.5940	9.8181	9.1285	8.5136
21	11.7641	10.8355	10.0168	9.2922	8.6487
22	12.0416	11.0612	10.2007	9.4424	8.7715
23	12.3034	11.2722	10.3711	9.5802	8.8832
24	12.5504	11.4693	10.5288	9.7066	8.9847
25	12.7834	11.6536	10.6748	9.8226	9.0770
26	13.0032	11.8258	10.8100	9.9290	9.1609
27	13.2105	11.9867	10.9352	10.0266	9.2372
28	13.4062	12.1371	11.0511	10.1161	9.3066
29	13.5907	12.2777	11.1584	10.1983	9.3696
30	13.7648	12.4090	11.2578	10.2737	9.4269
31	13.9291	12.5318	11.3498	10.3428	9.4790
32	14.0840	12.6466	11.4350	10.4062	9.5264
33	14.2302	12.7538	11.5139	10.4644	9.5694
34	14.3681	12.8540	11.5869	10.5178	9.6086
35	14.4982	12.9477	11.6546	10.5668	9.6442
36	14.6210	13.0352	11.7172	10.6118	9.6765
37	14.7368	13.1170	11.7752	10.6530	9.7059
38	14.8460	13.1935	11.8289	10.6908	9.7327
39	14.9491	13.2649	11.8786	10.7255	9.7570
40	15.0463	13.3317	11.9246	10.7574	9.7791
41	15.1380	13.3941	11.9672	10.7866	9.7991
42	15.2245	13.4524	12.0067	10.8133	9.8174
43	15.3062	13.5070	12.0432	10.8380	9.8340
44	15.3832	13.5579	12.0771	10.8605	9.8491
45	15.4558	13.6055	12.1084	10.8812	9.8628
46	15.5244	13.6500	12.1374	10.9002	9.8753
47	15.5890	13.6916	12.1643	10.9176	9.8866
48	15.6500	13.7305	12.1892	10.9336	9.8969
49	15.7076	13.7668	12.2122	10.9482	9.9063
50	15.7619	13.8007	12.2335	10.9617	9.9148

11%~15%

年金現值係數表　

利率 —— 期數	11%	12%	13%	14%	15%
1	0.9009	0.8929	0.8850	0.8772	0.8696
2	1.7125	1.6901	1.6681	1.6466	1.6257
3	2.4437	2.4018	2.3612	2.3216	2.2832
4	3.1024	3.0373	2.9745	2.9137	2.8550
5	3.6958	3.6048	3.5172	3.4331	3.3522
6	4.2305	4.1114	3.9975	3.8887	3.7845
7	4.7122	4.5638	4.4226	4.2883	4.1604
8	5.1461	4.9676	4.7988	4.6389	4.4873
9	5.5370	5.3282	5.1317	4.9464	4.7716
10	5.8892	5.6502	5.4262	5.2161	5.0188
11	6.2065	5.9377	5.6869	5.4527	5.2337
12	6.4924	6.1944	5.9176	5.6603	5.4206
13	6.7499	6.4235	6.1218	5.8424	5.5831
14	6.9819	6.6282	6.3025	6.0021	5.7245
15	7.1909	6.8109	6.4624	6.1422	5.8474
16	7.3792	6.9740	6.6039	6.2651	5.9542
17	7.5488	7.1196	6.7291	6.3729	6.0472
18	7.7016	7.2497	6.8399	6.4674	6.1280
19	7.8393	7.3657	6.9380	6.5504	6.1982
20	7.9633	7.4694	7.0248	6.6231	6.2593
21	8.0751	7.5620	7.1016	6.6870	6.3125
22	8.1757	7.6446	7.1695	6.7429	6.3587
23	8.2664	7.7184	7.2297	6.7921	6.3988
24	8.3481	7.7843	7.2829	6.8351	6.4338
25	8.4217	7.8431	7.3300	6.8729	6.4641
26	8.4881	7.8957	7.3717	6.9061	6.4906
27	8.5478	7.9426	7.4086	6.9352	6.5135
28	8.6016	7.9844	7.4412	6.9607	6.5335
29	8.6501	8.0218	7.4701	6.9830	6.5509
30	8.6938	8.0552	7.4957	7.0027	6.5660
31	8.7331	8.0850	7.5183	7.0199	6.5791
32	8.7686	8.1116	7.5382	7.0350	6.5905
33	8.8005	8.1354	7.5560	7.0482	6.6005
34	8.8293	8.1566	7.5717	7.0599	6.6091
35	8.8552	8.1755	7.5856	7.0700	6.6166
36	8.8786	8.1924	7.5979	7.0790	6.6231
37	8.8996	8.2075	7.6087	7.0868	6.6288
38	8.9186	8.2210	7.6183	7.0937	6.6338
39	8.9357	8.2330	7.6268	7.0997	6.6380
40	8.9511	8.2438	7.6344	7.1050	6.6418
41	8.9649	8.2534	7.6410	7.1097	6.6450
42	8.9774	8.2619	7.6469	7.1138	6.6478
43	8.9886	8.2696	7.6522	7.1173	6.6503
44	8.9988	8.2764	7.6568	7.1205	6.6524
45	9.0079	8.2825	7.6609	7.1232	6.6543
46	9.0161	8.2880	7.6645	7.1256	6.6559
47	9.0235	8.2928	7.6677	7.1277	6.6573
48	9.0302	8.2972	7.6705	7.1296	6.6585
49	9.0362	8.3010	7.6730	7.1312	6.6596
50	9.0417	8.3045	7.6752	7.1327	6.6605

16%~20%

年金現值係數表　

利率 —— 期數	16%	17%	18%	19%	20%
1	0.8621	0.8547	0.8475	0.8403	0.8333
2	1.6052	1.5852	1.5656	1.5465	1.5278
3	2.2459	2.2096	2.1743	2.1399	2.1065
4	2.7982	2.7432	2.6901	2.6386	2.5887
5	3.2743	3.1993	3.1272	3.0576	2.9906
6	3.6847	3.5892	3.4976	3.4098	3.3255
7	4.0386	3.9224	3.8115	3.7057	3.6046
8	4.3436	4.2072	4.0776	3.9544	3.8372
9	4.6065	4.4506	4.3030	4.1633	4.0310
10	4.8332	4.6586	4.4941	4.3389	4.1925
11	5.0286	4.8364	4.6560	4.4865	4.3271
12	5.1971	4.9884	4.7932	4.6105	4.4392
13	5.3423	5.1183	4.9095	4.7147	4.5327
14	5.4675	5.2293	5.0081	4.8023	4.6106
15	5.5755	5.3242	5.0916	4.8759	4.6755
16	5.6685	5.4053	5.1624	4.9377	4.7296
17	5.7487	5.4746	5.2223	4.9897	4.7746
18	5.8178	5.5339	5.2732	5.0333	4.8122
19	5.8775	5.5845	5.3162	5.0700	4.8435
20	5.9288	5.6278	5.3527	5.1009	4.8696
21	5.9731	5.6647	5.3837	5.1268	4.8913
22	6.0113	5.6964	5.4099	5.1486	4.9094
23	6.0442	5.7234	5.4321	5.1668	4.9245
24	6.0726	5.7465	5.4509	5.1822	4.9371
25	6.0971	5.7662	5.4669	5.1951	4.9475
26	6.1182	5.7831	5.4804	5.2060	4.9563
27	6.1364	5.7975	5.4919	5.2151	4.9636
28	6.1520	5.8099	5.5016	5.2228	4.9697
29	6.1656	5.8204	5.5098	5.2292	4.9747
30	6.1772	5.8294	5.5168	5.2347	4.9789
31	6.1872	5.8371	5.5227	5.2392	4.9824
32	6.1958	5.8437	5.5277	5.2430	4.9854
33	6.2034	5.8493	5.5320	5.2462	4.9878
34	6.2098	5.8541	5.5356	5.2489	4.9898
35	6.2153	5.8582	5.5386	5.2512	4.9915
36	6.2201	5.8617	5.5412	5.2531	4.9929
37	6.2242	5.8647	5.5434	5.2547	4.9941
38	6.2278	5.8673	5.5452	5.2561	4.9951
39	6.2309	5.8695	5.5468	5.2572	4.9959
40	6.2335	5.8713	5.5482	5.2582	4.9966
41	6.2358	5.8729	5.5493	5.2590	4.9972
42	6.2377	5.8743	5.5502	5.2596	4.9976
43	6.2394	5.8755	5.5510	5.2602	4.9980
44	6.2409	5.8765	5.5517	5.2607	4.9984
45	6.2421	5.8773	5.5523	5.2611	4.9986
46	6.2432	5.8781	5.5528	5.2614	4.9989
47	6.2442	5.8787	5.5532	5.2617	4.9991
48	6.2450	5.8792	5.5536	5.2619	4.9992
49	6.2457	5.8797	5.5539	5.2621	4.9993
50	6.2463	5.8801	5.5541	5.2623	4.9995

21%~25%

年金現值係數表

利率 —— 期數	21%	22%	23%	24%	25%
1	0.8264	0.8197	0.8130	0.8065	0.8000
2	1.5095	1.4915	1.4740	1.4568	1.4400
3	2.0739	2.0422	2.0114	1.9813	1.9520
4	2.5404	2.4936	2.4483	2.4043	2.3616
5	2.9260	2.8636	2.8035	2.7454	2.6893
6	3.2446	3.1669	3.0923	3.0205	2.9514
7	3.5079	3.4155	3.3270	3.2423	3.1611
8	3.7256	3.6193	3.5179	3.4212	3.3289
9	3.9054	3.7863	3.6731	3.5655	3.4631
10	4.0541	3.9232	3.7993	3.6819	3.5705
11	4.1769	4.0354	3.9018	3.7757	3.6564
12	4.2784	4.1274	3.9852	3.8514	3.7251
13	4.3624	4.2028	4.0530	3.9124	3.7801
14	4.4317	4.2646	4.1082	3.9616	3.8241
15	4.4890	4.3152	4.1530	4.0013	3.8593
16	4.5364	4.3567	4.1894	4.0333	3.8874
17	4.5755	4.3908	4.2190	4.0591	3.9099
18	4.6079	4.4187	4.2431	4.0799	3.9279
19	4.6346	4.4415	4.2627	4.0967	3.9424
20	4.6566	4.4603	4.2786	4.1103	3.9539
21	4.6750	4.4756	4.2916	4.1212	3.9631
22	4.6900	4.4882	4.3021	4.1300	3.9705
23	4.7025	4.4985	4.3106	4.1371	3.9764
24	4.7128	4.5070	4.3176	4.1428	3.9811
25	4.7213	4.5139	4.3232	4.1474	3.9849
26	4.7284	4.5196	4.3278	4.1511	3.9879
27	4.7342	4.5243	4.3316	4.1542	3.9903
28	4.7390	4.5281	4.3346	4.1566	3.9923
29	4.7430	4.5312	4.3371	4.1585	3.9938
30	4.7463	4.5338	4.3391	4.1601	3.9950
31	4.7490	4.5359	4.3407	4.1614	3.9960
32	4.7512	4.5376	4.3421	4.1624	3.9968
33	4.7531	4.5390	4.3431	4.1632	3.9975
34	4.7546	4.5402	4.3440	4.1639	3.9980
35	4.7559	4.5411	4.3447	4.1644	3.9984
36	4.7569	4.5419	4.3453	4.1649	3.9987
37	4.7578	4.5426	4.3458	4.1652	3.9990
38	4.7585	4.5431	4.3462	4.1655	3.9992
39	4.7590	4.5435	4.3465	4.1657	3.9993
40	4.7596	4.5439	4.3467	4.1659	3.9995
41	4.7600	4.5441	4.3469	4.1661	3.9996
42	4.7603	4.5444	4.3471	4.1662	3.9997
43	4.7606	4.5446	4.3472	4.1663	3.9997
44	4.7608	4.5447	4.3473	4.1663	3.9998
45	4.7610	4.5448	4.3474	4.1664	3.9998
46	4.7612	4.5450	4.3475	4.1665	3.9999
47	4.7613	4.5451	4.3476	4.1665	3.9999
48	4.7614	4.5451	4.3476	4.1665	3.9999
49	4.7615	4.5452	4.3477	4.1666	3.9999
50	4.7616	4.5452	4.3477	4.1666	3.9999

26%~30%

年金現值係數表　

利率 —— 期數	26%	27%	28%	29%	30%
1	0.7937	0.7874	0.7813	0.7752	0.7692
2	1.4235	1.4074	1.3916	1.3761	1.3609
3	1.9234	1.8956	1.8684	1.8420	1.8161
4	2.3202	2.2800	2.2410	2.2031	2.1662
5	2.6351	2.5827	2.5320	2.4830	2.4356
6	2.8850	2.8210	2.7594	2.7000	2.6427
7	3.0833	3.0087	2.9370	2.8682	2.8021
8	3.2407	3.1564	3.0758	2.9986	2.9247
9	3.3657	3.2728	3.1842	3.0997	3.0190
10	3.4648	3.3644	3.2689	3.1780	3.0915
11	3.5435	3.4365	3.3351	3.2388	3.1473
12	3.6059	3.4933	3.3868	3.2859	3.1903
13	3.6555	3.5381	3.4272	3.3224	3.2233
14	3.6949	3.5733	3.4587	3.3507	3.2487
15	3.7261	3.6010	3.4834	3.3726	3.2682
16	3.7509	3.6228	3.5026	3.3896	3.2832
17	3.7705	3.6400	3.5177	3.4028	3.2948
18	3.7861	3.6536	3.5294	3.4130	3.3037
19	3.7985	3.6642	3.5386	3.4210	3.3105
20	3.8083	3.6726	3.5458	3.4271	3.3158
21	3.8161	3.6792	3.5514	3.4318	3.3198
22	3.8223	3.6844	3.5558	3.4356	3.3230
23	3.8273	3.6885	3.5592	3.4384	3.3254
24	3.8312	3.6918	3.5619	3.4406	3.3272
25	3.8342	3.6943	3.5640	3.4423	3.3286
26	3.8367	3.6963	3.5656	3.4437	3.3297
27	3.8387	3.6979	3.5669	3.4447	3.3306
28	3.8402	3.6991	3.5679	3.4455	3.3312
29	3.8414	3.7001	3.5687	3.4461	3.3317
30	3.8424	3.7009	3.5693	3.4466	3.3321
31	3.8432	3.7015	3.5697	3.4470	3.3324
32	3.8438	3.7019	3.5701	3.4473	3.3326
33	3.8443	3.7023	3.5704	3.4475	3.3328
34	3.8447	3.7026	3.5706	3.4477	3.3329
35	3.8450	3.7028	3.5708	3.4478	3.3330
36	3.8452	3.7030	3.5709	3.4479	3.3331
37	3.8454	3.7032	3.5710	3.4480	3.3331
38	3.8456	3.7033	3.5711	3.4481	3.3332
39	3.8457	3.7034	3.5712	3.4481	3.3332
40	3.8458	3.7034	3.5712	3.4481	3.3332
41	3.8459	3.7035	3.5713	3.4482	3.3333
42	3.8459	3.7035	3.5713	3.4482	3.3333
43	3.8460	3.7036	3.5713	3.4482	3.3333
44	3.8460	3.7036	3.5714	3.4482	3.3333
45	3.8460	3.7036	3.5714	3.4482	3.3333
46	3.8461	3.7036	3.5714	3.4482	3.3333
47	3.8461	3.7037	3.5714	3.4483	3.3333
48	3.8461	3.7037	3.5714	3.4483	3.3333
49	3.8461	3.7037	3.5714	3.4483	3.3333
50	3.8461	3.7037	3.5714	3.4483	3.3333

31%~35%

年金現值係數表

利率 —— 期數	31%	32%	33%	34%	35%
1	0.7634	0.7576	0.7519	0.7463	0.7407
2	1.3461	1.3315	1.3172	1.3032	1.2894
3	1.7909	1.7663	1.7423	1.7188	1.6959
4	2.1305	2.0957	2.0618	2.0290	1.9969
5	2.3897	2.3452	2.3021	2.2604	2.2200
6	2.5875	2.5342	2.4828	2.4331	2.3852
7	2.7386	2.6775	2.6187	2.5620	2.5075
8	2.8539	2.7860	2.7208	2.6582	2.5982
9	2.9419	2.8681	2.7976	2.7300	2.6653
10	3.0091	2.9304	2.8553	2.7836	2.7150
11	3.0604	2.9776	2.8987	2.8236	2.7519
12	3.0995	3.0133	2.9313	2.8534	2.7792
13	3.1294	3.0404	2.9559	2.8757	2.7994
14	3.1522	3.0609	2.9744	2.8923	2.8144
15	3.1696	3.0764	2.9883	2.9047	2.8255
16	3.1829	3.0882	2.9987	2.9140	2.8337
17	3.1931	3.0971	3.0065	2.9209	2.8398
18	3.2008	3.1039	3.0124	2.9260	2.8443
19	3.2067	3.1090	3.0169	2.9299	2.8476
20	3.2112	3.1129	3.0202	2.9327	2.8501
21	3.2147	3.1158	3.0227	2.9349	2.8519
22	3.2173	3.1180	3.0246	2.9365	2.8533
23	3.2193	3.1197	3.0260	2.9377	2.8543
24	3.2209	3.1210	3.0271	2.9386	2.8550
25	3.2220	3.1220	3.0279	2.9392	2.8556
26	3.2229	3.1227	3.0285	2.9397	2.8560
27	3.2236	3.1233	3.0289	2.9401	2.8563
28	3.2241	3.1237	3.0293	2.9404	2.8565
29	3.2245	3.1240	3.0295	2.9406	2.8567
30	3.2248	3.1242	3.0297	2.9407	2.8568
31	3.2251	3.1244	3.0299	2.9408	2.8569
32	3.2252	3.1246	3.0300	2.9409	2.8569
33	3.2254	3.1247	3.0301	2.9410	2.8570
34	3.2255	3.1248	3.0301	2.9410	2.8570
35	3.2256	3.1248	3.0302	2.9411	2.8571
36	3.2256	3.1249	3.0302	2.9411	2.8571
37	3.2257	3.1249	3.0302	2.9411	2.8571
38	3.2257	3.1249	3.0302	2.9411	2.8571
39	3.2257	3.1249	3.0303	2.9411	2.8571
40	3.2257	3.1250	3.0303	2.9412	2.8571
41	3.2258	3.1250	3.0303	2.9412	2.8571
42	3.2258	3.1250	3.0303	2.9412	2.8571
43	3.2258	3.1250	3.0303	2.9412	2.8571
44	3.2258	3.1250	3.0303	2.9412	2.8571
45	3.2258	3.1250	3.0303	2.9412	2.8571
46	3.2258	3.1250	3.0303	2.9412	2.8571
47	3.2258	3.1250	3.0303	2.9412	2.8571
48	3.2258	3.1250	3.0303	2.9412	2.8571
49	3.2258	3.1250	3.0303	2.9412	2.8571
50	3.2258	3.1250	3.0303	2.9412	2.8571

36%~40%

年金現值信息表　

利率 —— 期數	36%	37%	38%	39%	40%
1	0.7353	0.7299	0.7246	0.7194	0.7143
2	1.2760	1.2627	1.2497	1.2370	1.2245
3	1.6735	1.6516	1.6302	1.6093	1.5889
4	1.9658	1.9355	1.9060	1.8772	1.8492
5	2.1808	2.1427	2.1058	2.0699	2.0352
6	2.3388	2.2939	2.2506	2.2086	2.1680
7	2.4550	2.4043	2.3555	2.3083	2.2628
8	2.5404	2.4849	2.4315	2.3801	2.3306
9	2.6033	2.5437	2.4866	2.4317	2.3790
10	2.6495	2.5867	2.5265	2.4689	2.4136
11	2.6834	2.6180	2.5555	2.4956	2.4383
12	2.7084	2.6409	2.5764	2.5148	2.4559
13	2.7268	2.6576	2.5916	2.5286	2.4685
14	2.7403	2.6698	2.6026	2.5386	2.4775
15	2.7502	2.6787	2.6106	2.5457	2.4839
16	2.7575	2.6852	2.6164	2.5509	2.4885
17	2.7629	2.6899	2.6206	2.5546	2.4918
18	2.7668	2.6934	2.6236	2.5573	2.4941
19	2.7697	2.6959	2.6258	2.5592	2.4958
20	2.7718	2.6977	2.6274	2.5606	2.4970
21	2.7734	2.6991	2.6286	2.5616	2.4979
22	2.7746	2.7000	2.6294	2.5623	2.4985
23	2.7754	2.7008	2.6300	2.5628	2.4989
24	2.7760	2.7013	2.6304	2.5632	2.4992
25	2.7765	2.7017	2.6307	2.5634	2.4994
26	2.7768	2.7019	2.6310	2.5636	2.4996
27	2.7771	2.7022	2.6311	2.5637	2.4997
28	2.7773	2.7023	2.6313	2.5638	2.4998
29	2.7774	2.7024	2.6313	2.5639	2.4999
30	2.7775	2.7025	2.6314	2.5640	2.4999
31	2.7776	2.7025	2.6315	2.5640	2.4999
32	2.7776	2.7026	2.6315	2.5640	2.4999
33	2.7777	2.7026	2.6315	2.5641	2.5000
34	2.7777	2.7026	2.6315	2.5641	2.5000
35	2.7777	2.7027	2.6315	2.5641	2.5000
36	2.7777	2.7027	2.6316	2.5641	2.5000
37	2.7777	2.7027	2.6316	2.5641	2.5000
38	2.7778	2.7027	2.6316	2.5641	2.5000
39	2.7778	2.7027	2.6316	2.5641	2.5000
40	2.7778	2.7027	2.6316	2.5641	2.5000
41	2.7778	2.7027	2.6316	2.5641	2.5000
42	2.7778	2.7027	2.6316	2.5641	2.5000
43	2.7778	2.7027	2.6316	2.5641	2.5000
44	2.7778	2.7027	2.6316	2.5641	2.5000
45	2.7778	2.7027	2.6316	2.5641	2.5000
46	2.7778	2.7027	2.6316	2.5641	2.5000
47	2.7778	2.7027	2.6316	2.5641	2.5000
48	2.7778	2.7027	2.6316	2.5641	2.5000
49	2.7778	2.7027	2.6316	2.5641	2.5000
50	2.7778	2.7027	2.6316	2.5641	2.5000

41%~45%

年金現值係數表

利率 —— 期數	41%	42%	43%	44%	45%
1	0.7092	0.7042	0.6993	0.6944	0.6897
2	1.2122	1.2002	1.1883	1.1767	1.1652
3	1.5689	1.5494	1.5303	1.5116	1.4933
4	1.8219	1.7954	1.7694	1.7442	1.7195
5	2.0014	1.9686	1.9367	1.9057	1.8755
6	2.1286	2.0905	2.0536	2.0178	1.9831
7	2.2189	2.1764	2.1354	2.0957	2.0573
8	2.2829	2.2369	2.1926	2.1498	2.1085
9	2.3283	2.2795	2.2326	2.1874	2.1438
10	2.3605	2.3095	2.2605	2.2134	2.1681
11	2.3833	2.3307	2.2801	2.2316	2.1849
12	2.3995	2.3455	2.2938	2.2441	2.1965
13	2.4110	2.3560	2.3033	2.2529	2.2045
14	2.4192	2.3634	2.3100	2.2589	2.2100
15	2.4249	2.3686	2.3147	2.2632	2.2138
16	2.4290	2.3722	2.3180	2.2661	2.2164
17	2.4319	2.3748	2.3203	2.2681	2.2182
18	2.4340	2.3766	2.3219	2.2695	2.2195
19	2.4355	2.3779	2.3230	2.2705	2.2203
20	2.4365	2.3788	2.3238	2.2712	2.2209
21	2.4372	2.3794	2.3243	2.2717	2.2213
22	2.4377	2.3799	2.3247	2.2720	2.2216
23	2.4381	2.3802	2.3250	2.2722	2.2218
24	2.4384	2.3804	2.3251	2.2724	2.2219
25	2.4386	2.3806	2.3253	2.2725	2.2220
26	2.4387	2.3807	2.3254	2.2726	2.2221
27	2.4388	2.3808	2.3254	2.2726	2.2221
28	2.4389	2.3808	2.3255	2.2726	2.2222
29	2.4389	2.3809	2.3255	2.2727	2.2222
30	2.4389	2.3809	2.3255	2.2727	2.2222
31	2.4390	2.3809	2.3255	2.2727	2.2222
32	2.4390	2.3809	2.3256	2.2727	2.2222
33	2.4390	2.3809	2.3256	2.2727	2.2222
34	2.4390	2.3809	2.3256	2.2727	2.2222
35	2.4390	2.3809	2.3256	2.2727	2.2222
36	2.4390	2.3809	2.3256	2.2727	2.2222
37	2.4390	2.3809	2.3256	2.2727	2.2222
38	2.4390	2.3809	2.3256	2.2727	2.2222
39	2.4390	2.3809	2.3256	2.2727	2.2222
40	2.4390	2.3810	2.3256	2.2727	2.2222
41	2.4390	2.3810	2.3256	2.2727	2.2222
42	2.4390	2.3810	2.3256	2.2727	2.2222
43	2.4390	2.3810	2.3256	2.2727	2.2222
44	2.4390	2.3810	2.3256	2.2727	2.2222
45	2.4390	2.3810	2.3256	2.2727	2.2222
46	2.4390	2.3810	2.3256	2.2727	2.2222
47	2.4390	2.3810	2.3256	2.2727	2.2222
48	2.4390	2.3810	2.3256	2.2727	2.2222
49	2.4390	2.3810	2.3256	2.2727	2.2222
50	2.4390	2.3810	2.3256	2.2727	2.2222

46%~50%

年金現值係數表

利率 —— 期數	46%	47%	48%	49%	50%
1	0.6849	0.6803	0.6757	0.6711	0.6667
2	1.1541	1.1430	1.1322	1.1216	1.1111
3	1.4754	1.4579	1.4407	1.4239	1.4074
4	1.6955	1.6720	1.6491	1.6268	1.6049
5	1.8462	1.8177	1.7899	1.7629	1.7366
6	1.9495	1.9168	1.8851	1.8543	1.8244
7	2.0202	1.9842	1.9494	1.9156	1.8829
8	2.0686	2.0301	1.9928	1.9568	1.9220
9	2.1018	2.0613	2.0222	1.9844	1.9480
10	2.1245	2.0825	2.0420	2.0030	1.9653
11	2.1401	2.0969	2.0554	2.0154	1.9769
12	2.1507	2.1068	2.0645	2.0237	1.9846
13	2.1580	2.1134	2.0706	2.0294	1.9897
14	2.1630	2.1180	2.0747	2.0331	1.9931
15	2.1665	2.1211	2.0775	2.0357	1.9954
16	2.1688	2.1232	2.0794	2.0374	1.9970
17	2.1704	2.1246	2.0807	2.0385	1.9980
18	2.1715	2.1256	2.0815	2.0393	1.9986
19	2.1723	2.1263	2.0821	2.0398	1.9991
20	2.1728	2.1267	2.0825	2.0401	1.9994
21	2.1731	2.1270	2.0828	2.0403	1.9996
22	2.1734	2.1272	2.0830	2.0405	1.9997
23	2.1736	2.1274	2.0831	2.0406	1.9998
24	2.1737	2.1275	2.0832	2.0407	1.9999
25	2.1737	2.1275	2.0832	2.0407	1.9999
26	2.1738	2.1276	2.0833	2.0408	1.9999
27	2.1738	2.1276	2.0833	2.0408	2.0000
28	2.1739	2.1276	2.0833	2.0408	2.0000
29	2.1739	2.1276	2.0833	2.0408	2.0000
30	2.1739	2.1276	2.0833	2.0408	2.0000
31	2.1739	2.1276	2.0833	2.0408	2.0000
32	2.1739	2.1277	2.0833	2.0408	2.0000
33	2.1739	2.1277	2.0833	2.0408	2.0000
34	2.1739	2.1277	2.0833	2.0408	2.0000
35	2.1739	2.1277	2.0833	2.0408	2.0000
36	2.1739	2.1277	2.0833	2.0408	2.0000
37	2.1739	2.1277	2.0833	2.0408	2.0000
38	2.1739	2.1277	2.0833	2.0408	2.0000
39	2.1739	2.1277	2.0833	2.0408	2.0000
40	2.1739	2.1277	2.0833	2.0408	2.0000
41	2.1739	2.1277	2.0833	2.0408	2.0000
42	2.1739	2.1277	2.0833	2.0408	2.0000
43	2.1739	2.1277	2.0833	2.0408	2.0000
44	2.1739	2.1277	2.0833	2.0408	2.0000
45	2.1739	2.1277	2.0833	2.0408	2.0000
46	2.1739	2.1277	2.0833	2.0408	2.0000
47	2.1739	2.1277	2.0833	2.0408	2.0000
48	2.1739	2.1277	2.0833	2.0408	2.0000
49	2.1739	2.1277	2.0833	2.0408	2.0000
50	2.1739	2.1277	2.0833	2.0408	2.0000

作用

計算貨幣價值

已知年金和係數，計算年金現值，得出某一時點貨幣的價值，這是年金現值的基本作用。

比較投資方案

根據貨幣價值的不同，可以比較投資方案/籌資方案的優劣。

比較方案優劣

不同年限、不同投資/籌資總額的方案可以通過計算年金淨現值（ANPV）指標進行方案優劣比較。

計算報酬率

通過插值法可以計算出籌資內含報酬率（IRR）。