年金現值

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。

基本介紹

  • 中文名：年金現值
  • 外文名：Present Value of Annuity
  • 屬於：會計學
  • 種類：普通年金現值、先付年金現值
  • 種類：遞延年金現值、永續年金現值
分類,計算,普通年金現值,先付年金現值,遞延年金現值,永續年金現值,係數表,作用,計算貨幣價值,比較投資方案,比較方案優劣,計算報酬率,

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?
公式推導如下：
兩邊同時乘以
得
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：
。
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：

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

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
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）。

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