年金終值

年金終值

年金終值就是在已知等額收付款金額Present、利率（這裡我們默認為年利率）interest和計息期數n時，考慮貨幣的時間價值，計算出的這些收付款到到期時的等價票面金額。

而年金按其每次收付發生的時點（即收付當日日是在①有限期的首期期末、②有限期的首期期初、③有限期的若干期後的期末、④無限期）的不同，可分為：普通年金（後付年金）、先付年金、遞延年金、永續年金等幾種，故年金終值亦可分為：普通年金終值、先付年金終值、遞延年金終值。（註：永續年金只有現值，不存在終值。）

基本介紹

  • 中文名：年金終值
  • 外文名：Final Value\Amount of the Annuity
  • 概念：一定期間內每期等額收付的款項
  • 普通年金：每期期末收付款項的年金
  • 先付年金：每期期初收付款項的年金
  • 遞延年金：未來會發生若干期等額收付的年金
  • 永續年金：無限期連續收付款的年金
概念與分類,概念,分類,背景,分類與計算,普通年金終值,先付年金終值,遞延年金終值,永續年金終值,係數表,

概念與分類

概念

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）。

分類

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。

背景

從資本主義初期開始，“高利貸”現象頻出，貸出資金者在短時期內“利滾利”生錢，由此也就產生了“複利”的概念。在這樣的社會大背景下，複利產生了；而為了簡化等額複利的計算，年金也就應運而生。

分類與計算

普通年金終值

普通年金終值：指一定時期內，每期期末等額收入或支出的本利和，也就是將每一期的金額，按複利換算到最後一期期末的終值，然後加總，就是該年金終值。例如：每年存款10000元，年利率為10%，經過5年，逐年的終值為年金終值，計算為：
記作F=A（F/A，i，n）。推導如下：
如果年金的期數n很多，用上述方法計算終值顯然相當繁瑣。由於每年支付額相等，折算終值的係數又是有規律的，所以，可找出簡便的計算方法，其思路為：將其視為以（1+i）為公比的等比數列，採用等比數列求和公式，將其簡化為以下公式：
設每年的支付金額為A，利率為i，期數為n，則按複利計算的年金終值F為：
式中
為普通年金終值係數後付年金終值係數，利率為i，經過n期的年金終值記作(F/A，i，n)，可查普通年金終值係數表。

先付年金終值

先付年金終值：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終值之和。
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期先付年金終值比n期普通年金的終值多計算一期利息。因此在n期普通年金終值的基礎上乘以（1+i）就得出n期先付年金的終值了，公式為：
記作F=A·[(F/A，i，n+1)-1]
則如果上例為每年初計息的話，經過5年，逐年的終值為年金終值，計算為：

遞延年金終值

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）

永續年金終值

永續年金因為是無限期收付的，所以永續年金沒有終值。

係數表

本詞條提供1%~50%利率1~50期的年金終值係數（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）
年 金 終 值 系 數 表
利率
——
期數		1%2%3%4%5%
1
1.0000
1.0000
1.0000
1.0000
1.0000
2
2.0100
2.0200
2.0300
2.0400
2.0500
3
3.0301
3.0604
3.0909
3.1216
3.1525
4
4.0604
4.1216
4.1836
4.2465
4.3101
5
5.1010
5.2040
5.3091
5.4163
5.5256
6
6.1520
6.3081
6.4684
6.6330
6.8019
7
7.2135
7.4343
7.6625
7.8983
8.1420
8
8.2856
8.5830
8.8923
9.2142
9.5491
9
9.3685
9.7546
10.1591
10.5828
11.0266
10
10.4622
10.9497
11.4639
12.0061
12.5779
11
11.5668
12.1687
12.8078
13.4864
14.2068
12
12.6825
13.4121
14.1920
15.0258
15.9171
13
13.8093
14.6803
15.6178
16.6268
17.7130
14
14.9474
15.9739
17.0863
18.2919
19.5986
15
16.0969
17.2934
18.5989
20.0236
21.5786
16
17.2579
18.6393
20.1569
21.8245
23.6575
17
18.4304
20.0121
21.7616
23.6975
25.8404
18
19.6147
21.4123
23.4144
25.6454
28.1324
19
20.8109
22.8406
25.1169
27.6712
30.5390
20
22.0190
24.2974
26.8704
29.7781
33.0660
21
23.2392
25.7833
28.6765
31.9692
35.7193
22
24.4716
27.2990
30.5368
34.2480
38.5052
23
25.7163
28.8450
32.4529
36.6179
41.4305
24
26.9735
30.4219
34.4265
39.0826
44.5020
25
28.2432
32.0303
36.4593
41.6459
47.7271
26
29.5256
33.6709
38.5530
44.3117
51.1135
27
30.8209
35.3443
40.7096
47.0842
54.6691
28
32.1291
37.0512
42.9309
49.9676
58.4026
29
33.4504
38.7933
45.3289
52.9663
62.3227
30
34.7849
40.5681
47.5754
56.0849
66.4388
31
36.1327
42.3794
50.0027
59.3283
70.7608
32
37.4941
44.2270
52.5028
62.7015
75.2988
33
38.8690
46.1116
55.0778
66.2095
80.0638
34
40.2577
48.0338
57.7302
69.8579
85.0670
35
41.6603
49.9945
60.4621
73.6522
90.3203
36
43.0769
51.9944
63.2759
77.5983
95.8363
37
44.5076
54.0343
66.1742
81.7022
101.6281
38
45.9527
56.1149
69.1594
85.9703
107.7095
39
47.4123
58.2372
72.2342
90.4091
114.0950
40
48.8864
60.4020
75.4013
95.0255
120.7998
41
50.3752
62.6100
78.6633
99.8265
127.8398
42
51.8790
64.8622
82.0232
104.8196
135.2318
43
53.3978
67.1595
85.4839
110.0124
142.9933
44
54.9318
69.5027
89.0484
115.4129
151.1430
45
54.4811
71.8927
92.7199
121.0294
159.7002
46
58.0459
74.3306
96.5015
126.8706
168.6852
47
59.6263
76.8172
100.3965
132.9454
178.1194
48
61.2226
79.3535
104.4084
139.2632
188.0254
49
62.8348
81.9406
108.5406
145.8337
198.4267
50
64.4632
84.5794
112.7969
152.6671
209.3480
表二（6%~10%利率）
年金終值係數表（續表一）
利率
——
期數		6%7%8%9%10%
1
1.0000
1.0000
1.0000
1.0000
1.0000
2
2.0600
2.0700
2.0800
2.0900
2.1000
3
3.1836
3.2149
3.2464
3.2781
3.3100
4
4.3746
4.4399
4.5061
4.5731
4.6410
5
5.6371
5.7507
5.8666
5.9847
6.1051
6
6.9753
7.1533
7.3359
7.5233
7.7156
7
8.3938
8.6540
8.9228
9.2004
9.4872
8
9.8975
10.2598
10.6366
11.0285
11.4359
9
11.4913
11.9780
12.4876
13.0210
13.5795
10
13.1808
13.8164
14.4866
15.1929
15.9374
11
14.9716
15.7836
16.6455
17.5603
18.5312
12
16.8699
17.8884
18.9771
20.1407
21.3843
13
18.8821
20.1406
21.4953
22.9534
24.5227
14
21.0151
22.5505
24.2149
26.0192
27.9750
15
23.2760
25.1290
27.1521
29.3609
31.7725
16
25.6725
27.8881
30.3243
33.0034
35.9497
17
28.2129
30.8402
33.7502
36.9737
40.5447
18
30.9057
33.9990
37.4502
41.3013
45.5992
19
33.7600
37.3790
41.4463
46.0185
51.1591
20
36.7856
40.9955
45.7620
51.1601
57.2750
21
39.9927
44.8652
50.4229
56.7645
64.0025
22
43.3923
49.0057
55.4568
62.8733
71.4027
23
46.9958
53.4361
60.8933
69.5319
79.5430
24
50.8156
58.1767
66.6748
76.7898
88.4873
25
54.8645
63.2490
73.1059
84.7009
98.3471
26
59.1564
68.6765
79.9544
93.3240
109.1818
27
63.7058
74.4838
87.3508
102.7231
121.0999
28
68.5281
80.6977
95.3388
112.9682
134.2099
29
73.6398
87.3465
103.9659
123.1354
148.6309
30
79.0582
94.4608
113.2832
136.3075
164.4940
31
84.8017
102.0730
123.3459
149.5752
181.9434
32
90.8898
110.2182
134.2135
164.0370
201.1378
33
97.3432
118.9334
145.9506
179.8003
222.2515
34
104.1838
128.2588
158.6267
196.9823
245.4767
35
111.4348
138.2369
172.3168
215.7108
271.0244
36
119.1209
148.9135
187.1021
236.1247
299.1268
37
127.2681
160.3374
203.0703
258.3759
330.0395
38
135.9042
172.5610
220.3159
282.6298
364.0434
39
145.0585
185.6403
238.9412
309.0665
401.4478
40
154.7620
199.6351
259.0565
337.8824
442.5926
41
165.0477
214.6096
280.7810
369.2919
487.8518
42
175.9505
230.6322
304.2435
403.5281
537.6370
43
187.5076
247.7765
329.5830
440.8457
592.4007
44
199.7580
266.1209
356.9496
481.5218
652.6408
45
212.7435
285.7493
386.5056
525.8587
718.9048
46
226.5081
306.7518
418.4261
574.1860
791.7953
47
241.0986
329.2244
452.9002
626.8628
871.9749
48
256.5645
353.2701
490.1322
684.2804
960.1723
49
272.9584
378.9990
530.3427
746.8656
1,057.1896
50
290.3359
406.5289
573.7702
815.0836
1,163.9085
表三（11%~15%利率）
年金終值係數表（續表二）
利率
——
期數		11%12%13%14%15%
1
1.0000
1.0000
1.0000
1.0000
1.0000
2
2.1100
2.1200
2.1300
2.1400
2.1500
3
3.3421
3.3744
3.4069
3.4396
3.4725
4
4.7097
4.7793
4.8498
4.9211
4.9934
5
6.2778
6.3528
6.4803
6.6101
6.7424
6
7.9129
8.1152
8.3227
8.5355
8.7537
7
9.7833
10.0890
10.4047
10.7305
11.0668
8
11.8594
12.2997
12.7573
13.2328
13.7268
9
14.1640
14.7757
15.4157
16.0853
16.7858
10
16.7220
17.5487
18.4197
19.3373
20.3037
11
19.5614
20.6546
21.8143
23.0445
24.3493
12
22.7132
24.1331
25.6502
27.2707
29.0017
13
26.2116
28.0291
29.9847
32.0887
34.3519
14
30.0949
32.3926
34.8827
37.5811
40.5047
15
34.4054
37.2797
40.4175
43.8424
47.5804
16
39.1899
42.7533
46.6717
50.9804
55.7175
17
44.5008
48.8837
53.7391
59.1176
65.0751
18
50.3959
55.7497
61.7251
68.3941
75.8364
19
56.9395
63.4397
70.7494
78.9692
88.2118
20
64.2028
72.0524
80.9468
91.0249
102.4436
21
72.2651
81.6987
92.4699
104.7684
118.8101
22
81.2143
92.5026
105.4910
120.4360
137.6316
23
91.1479
104.6029
120.2048
138.2970
159.2764
24
102.1742
118.1552
136.8315
158.6586
184.1678
25
114.4133
133.3339
155.6196
181.8708
212.7930
26
127.9988
150.3339
176.8501
208.3327
245.7120
27
143.0786
169.3740
200.8406
238.4993
283.5688
28
159.8173
190.6989
227.9499
272.8892
327.1041
29
178.3972
214.5828
258.5834
312.0937
377.1697
30
199.0209
241.3327
293.1992
356.7868
434.7451
31
221.9132
271.2926
332.3151
407.7370
500.9569
32
247.3236
304.8477
376.5161
465.8202
577.1005
33
275.5292
342.4294
426.4632
532.0350
664.6655
34
306.8374
384.5210
482.9034
607.5199
765.3654
35
341.5896
431.6635
546.6808
693.5727
881.1702
36
380.1644
484.4631
618.7493
791.6729
1,014.3457
37
422.9825
543.5987
700.1867
903.5071
1,167.4975
38
470.5106
609.8305
792.2110
1,030.9881
1,343.6222
39
523.2667
684.0102
896.1984
1,176.3378
1,546.1655
40
581.8261
767.0914
1,013.7042
1,342.0251
1,779.0903
41
646.8269
860.1424
1,146.4858
1,530.9086
2,046.9539
42
718.9779
964.3595
1,296.5289
1,746.2358
2,354.9969
43
799.0655
1,081.0826
1,466.0777
1,991.7088
2,709.2465
44
887.9627
1,211.8125
1,657.6678
2,271.5481
3,116.6334
45
986.6386
1,358.2300
1,874.1646
2,590.5648
3,585.1285
46
1,096.1688
1,522.2176
2,118.8060
2,954.2439
4,123.8977
47
1,217.7474
1,705.8838
2,395.2508
3,368.8380
4,743.4824
48
1,352.6996
1,911.5898
2,707.6334
3,841.4753
5,456.0047
49
1,502.4965
2,141.9806
3,060.6258
4,380.2819
6,275.4055
50
1,668.7712
2400.0182
3,459.5071
4,994.5213
7,217.7163
表四（16%~20%利率）
年金終值係數表（續表三）
利率
——
期數		16%17%18%19%20%
1
1.0000
1.0000
1.0000
1.0000
1.0000
2
2.1600
2.1700
2.1800
2.1900
2.2000
3
3.5056
3.5389
3.5724
3.6061
3.6400
4
5.0665
5.1405
5.2154
5.2913
5.3680
5
6.8771
7.0144
7.1542
7.2966
7.4416
6
8.9774
9.2068
9.4420
9.6830
9.9299
7
11.4139
11.7720
12.1415
12.5227
12.9159
8
14.2401
14.7733
15.3270
15.9020
16.4991
9
17.5185
18.2847
19.0859
19.9234
20.7989
10
21.3215
22.3931
23.5213
24.7089
25.9587
11
25.7329
27.1999
28.7551
30.4035
32.1504
12
30.8502
32.8239
34.9311
37.1802
39.5805
13
36.7862
39.4040
42.2187
45.2445
48.4966
14
43.6720
47.1027
50.8180
54.8409
59.1959
15
51.6595
56.1101
60.9653
66.2607
72.0351
16
60.9250
66.6488
72.9390
79.8502
87.4421
17
71.6730
78.9792
87.0680
96.0218
105.9306
18
84.1407
93.4056
103.7403
115.2659
128.1167
19
98.6032
110.2846
123.4135
138.1664
154.7400
20
115.3797
130.0329
146.6280
165.4180
186.6880
21
134.8405
153.1385
174.0210
197.8474
225.0256
22
157.4150
180.1721
206.3448
236.4385
271.0307
23
183.6014
211.8013
244.4868
282.3618
326.2369
24
213.9776
248.8076
289.4945
337.0105
392.4842
25
249.2140
292.1049
342.6035
402.0425
471.9811
26
290.0883
342.7627
405.2721
479.4306
567.3773
27
337.5024
402.0323
479.2211
571.5224
681.8528
28
392.5028
471.3778
566.4809
681.1116
819.2233
29
456.3032
552.5121
669.4475
811.5228
984.0680
30
530.3117
647.4391
790.9480
966.7122
1,181.8816
31
616.1616
758.5038
934.3186
1,151.3875
1,415.2579
32
715.7475
888.4494
1,103.4960
1,371.1511
1,704.1095
33
831.2671
1,040.4858
1,303.1253
1,632.6698
2,045.9314
34
965.2698
1,218.3684
1,538.6878
1,943.8771
2,456.1176
35
1,120.7130
1,426.4910
1,816.6516
2,314.2137
2,948.3411
36
1,301.0270
1,669.9945
2,144.6489
2,754.9143
3,539.0094
37
1,510.1914
1,954.8936
2,531.6857
3,279.3481
4,247.8113
38
1,752.8220
2,288.2255
2,988.3891
3,903.4242
5,098.3735
39
2,034.2735
2,678.2238
3,527.2992
4,646.0748
6,119.0482
40
2,360.7572
3,134.5218
4,163.2130
5,529.8290
7,343.8578
41
2,739.4784
3,668.3906
4,913.5914
6,581.4965
8,813.6294
42
3,178,7949
4,293.0169
5,799.0378
7,832.9808
10,577.3553
43
3,688.4021
5,023.8298
6,843.8646
9,322.2472
12,693.8264
44
4,279.5465
5,878.8809
8,076.7603
11,094.4741
15,233.5916
45
4,965.2739
6,879.2907
9,531.5771
13,203.4242
18,281.3099
46
5,760.7177
8,049.7701
11,248.2610
15,713.0748
21,938.5719
47
6,683.4326
9,419.2310
13,273.9479
18,699.5591
26,327.2863
48
7,753.7818
11,021.5002
15,664.2586
22,253.4753
31,593.7436
49
8,995.3869
12,896.1553
18,484.8251
26,482.6356
37,913.4923
50
10,435.6488
15,089.5017
21,813.0937
31,515.3363
45,497.1908
表五（21%~25%利率）
年金終值係數表（續表四）
利率
——
期數		21%22%23%24%25%
1
1.0000
1.0000
1.0000
1.0000
1.0000
2
2.2100
2.2200
2.2300
2.2400
2.2500
3
3.6741
3.7084
3.7429
3.7776
3.8125
4
5.4457
5.5242
5.5604
5.6842
5.7656
5
7.5892
7.7396
7.8926
8.0484
8.2070
6
10.1830
10.4423
10.7079
10.9801
11.2588
7
13.3214
13.7396
14.1708
14.6153
15.0735
8
17.1189
17.7623
18.4300
19.1229
19.8419
9
21.7139
22.6700
23.6690
24.7125
25.8023
10
27.2738
28.6574
30.1128
31.6434
33.2529
11
34.0013
35.9620
38.0388
40.2379
42.5661
12
42.1416
44.8737
47.7877
50.8950
54.2077
13
51.9913
55.7459
59.7788
64.1097
68.7596
14
63.9095
69.0100
74.5280
80.4961
86.9495
15
78.3305
85.1922
92.6694
100.8151
109.6868
16
95.7799
104.9345
114.9834
126.0108
138.1085
17
116.8937
129.0201
142.4295
157.2534
173.6357
18
142.4413
158.4045
176.1883
195.9942
218.0446
19
173.3540
194.2535
217.7116
244.0328
273.5558
20
210.7584
237.9893
268.7853
303.6006
342.9447
21
256.0176
291.3469
331.6059
377.4648
429.6809
22
310.7813
356.4432
408.8753
469.0563
538.1011
23
377.0454
435.8607
503.9166
582.6298
673.6264
24
457.2249
532.7501
620.8174
723.4610
843.0329
25
554.2422
650.9551
764.6054
898.0916
1,054.7912
26
671.6330
795.1653
941.4647
1,114.6336
1,319.4890
27
813.6759
971.1016
1,159.0016
1,383.1427
1,650.3612
28
985.5479
1,185.7440
1,426.5719
1,716.1007
2,063.9515
29
1,193.5129
1,447.6077
1,755.6835
2,128.9648
2,580.9394
30
1,445.1507
1,767.0813
2,160.4907
2,640.9164
3,227.1743
31
1,749.6323
2,156.8392
2,658.4036
3,275.7363
4,034.9678
32
2,118.0551
2,632.3439
3,270.8364
4,062.9130
5,044.7098
33
2,563.8467
3,212.4595
4,024.1287
5,039.0122
6,306.8872
34
3,103.2545
3,920.2006
4,950.6783
6,249.3751
7,884.6091
35
3,755.9379
4,783.6447
6,090.3344
7,750.2251
9,856.7613
36
4,545.6848
5,837.0466
7,492.1113
9,611.2791
12,321.9516
37
5,501.2787
7,122.1968
9,216.2969
11,918.9861
15,403.4396
38
6,657.5472
8,690.0801
11,337.0451
14,780.5428
19,255.2994
39
8,056.6321
10,602.8978
13,945.5655
18,328.8731
24,070.1243
40
9,749.5248
12,936.5353
17,154.0456
22,728.8026
30,088.6554
41
11,797.9251
15,783.5730
21,100.4761
28,184.7152
37,611.8192
42
14,276.4893
19,256.9591
25,954.5856
34,950.0469
47,015.7740
43
17,275.5521
23,494.4901
31,925.1403
43,339.0581
58,770.7175
44
20,904.4180
28,664.2779
39,268.9225
53,741.4321
73,464.3969
45
25,295.3458
34,971.4191
48,301.7747
66,640.3758
91,831.4962
46
30,608.3684
42,666.1312
59,412.1829
82,635.0660
114,790.3702
47
37,037.1257
52,053.6801
73,077.9850
102,468.4818
143,488.9627
48
44,815.9222
63,506.4897
89,886.9215
127,061.9174
179,362.2034
49
54,228.2658
77,478.9175
110,561.9135
157,557.7776
224,203.7543
50
65,617.2016
94,525.2793
135,992.1536
195,372.6442
280,255.6929
表六（26%~30%利率）
年金終值係數表（續表五）
利率
——
期數		26%27%28%29%30%
1
1.0000
1.0000
1.0000
1.0000
1.0000
2
2.2600
2.2700
2.2800
2.2900
2.3000
3
3.8476
3.8829
3.9184
3.9541
3.9900
4
5.8480
5.9313
6.0156
6.1008
6.1870
5
8.3684
8.5327
8.6999
8.8700
9.0431
6
11.5442
11.8366
12.1359
12.4423
12.7560
7
15.5458
16.0324
16.5339
17.0506
17.5828
8
20.5876
21.3612
22.1634
22.9953
23.8577
9
26.9404
28.1287
29.3692
30.6639
32.0150
10
34.9449
36.7235
38.5926
40.5564
42.6195
11
45.0306
47.6388
50.3985
53.3178
56.4053
12
57.7386
61.5013
65.5100
69.7800
74.3270
13
73.7506
79.1066
84.8529
91.0161
97.6250
14
93.9258
101.4654
109.6117
118.4108
127.9125
15
119.3465
129.8611
141.3029
153.7500
167.2863
16
151.3766
165.9236
181.8677
199.3374
218.4722
17
191.7345
211.7230
233.7907
258.1453
285.0139
18
242.5855
269.8882
300.2521
334.0074
371.5180
19
306.6577
343.7580
385.3227
431.8696
483.9734
20
387.3887
437.5726
494.2131
558.1118
630.1655
21
489.1098
556.7173
633.5927
720.9642
820.2151
22
617.2783
708.0309
811.9987
931.0438
1,067.2796
23
778.7707
900.1993
1,040.3583
1,202.0465
1,388.4635
24
982.2511
1,144.2531
1,332.6586
1,551.6400
1,806.0026
25
1,238.6363
1,454.2014
1,706.8031
2,002.6156
2,348.8033
26
1,561.6818
1,847.8358
2,185.7079
2,584.3741
3,054.4443
27
1,968.7191
2,347.7515
2,798.7061
3,334.8426
3,971.7776
28
2,481.5860
2,982.6444
3,583.3438
4,302.9470
5,164.3109
29
3,127.7984
3,788.9583
4,587.6801
5,551.8016
6,714.6042
30
3,942.0260
4,812.9771
5,873.2306
7,162.8241
8,279.9855
31
4,967.9527
6,113.4809
7,518.7351
9,241.0431
11,349.9811
32
6,260.6204
7,765.1207
9,624.9810
11,921.9456
14,755.9755
33
7,889.3817
9,862.7033
12,320.9756
15,380.3098
19,183.7681
34
9,941.6210
12,526.6332
15,771.8488
19,841.6000
24,939.8985
35
12,527.4424
15,909.8242
20,188.9665
25,596.6636
32,422.8681
36
15,785.5775
20,206.4767
25,842.8771
33,020.6960
42,150.7285
37
19,890.8276
25,663.2254
33,079.8826
42,597.6978
54,796.9471
38
25,063.4428
32,593,2963
42,343.2498
54,952.0302
71,237.0312
39
31,580.9379
41,394.4862
54,200.3597
70,889.1190
92,609.1045
40
39,792.9817
52,571.9976
69,377.4604
91,447.9635
120,392.8827
41
50,140.1569
66,767.4369
88,804.1494
117,968.8729
156,511.7475
42
63,177.5978
84,795.6449
113,670.3112
152,180.8460
203,466.2718
43
79,604.7732
107,691.4690
145,498.9983
196,314.2913
264,507.1533
44
100,303.0142
136,769.1656
186,239.7178
253,246.4358
343,860.2993
45
126,382.7979
173,697.8403
238,387.8388
326,688.9022
447,019.3890
46
159,243.3254
220,597.2572
305,137.4337
421,429.6838
581,126.2058
47
200,647.5900
280,159.5166
390,576.9151
543,645.2922
755,465.0675
48
252,816.9634
355,803.5861
499,939.4514
701,303.4269
982,105.5877
49
318,550.3739
451,871.5544
639,923.4978
904,682.4207
1,276,738.2640
50
401,374.4711
573,877.8741
819,103.0771
1,167,041.3227
1,659,760.7433
表七（31%~35%利率）
年金終值係數表（續表六）
利率
——
期數		31%32%33%34%35%
1
1.0000
1.0000
1.0000
1.0000
1.0000
2
2.3100
2.3200
2.3300
2.3400
2.3500
3
4.0261
4.0624
4.0989
4.1356
4.1725
4
6.2742
6.3624
6.4515
6.5417
6.6329
5
9.2192
9.3983
9.5805
9.7659
9.9544
6
13.0771
13.4058
13.7421
14.0863
14.4384
7
18.1311
18.6956
19.2770
19.8756
20.4919
8
24.7517
25.6782
26.6384
27.6333
28.6640
9
33.4247
34.8953
36.4291
38.0287
39.6964
10
44.7864
47.0618
49.4507
51.9584
54.5902
11
59.6701
63.1215
66.7695
70.6243
74.6967
12
79.1679
84.3204
89.8034
95.6365
101.8406
13
104.7099
112.3030
120.4385
129.1529
138.4848
14
138.1700
149.2399
161.1833
174.0649
187.9544
15
161.2024
197.9967
215.3737
234.2470
254.7385
16
239.4235
262.3557
287.4471
314.8910
344.8970
17
314.6448
347.3095
383.3046
422.9539
466.6109
18
413.1847
459.4485
510.7951
567.7583
630.9247
19
542.2719
607.7207
680.3575
761.7961
852.7483
20
711.3762
802.8631
905.8755
1,021.8068
1,152.2103
21
932.9028
1,060.7793
1,205.8144
1,370.2210
1,556.4838
22
1,223.1027
1,401.2287
1,604.7332
1,837.0962
2,102.2532
23
1,603.2645
1,850.6219
2,135.2951
2,462.7089
2,839.0418
24
2,101.2765
2,443.8209
2,840.9425
3,301.0300
3,833.7064
25
2,753.6722
3,226.8436
3,779.4536
4,424.3801
5,176.5037
26
3,608.3106
4,260.4336
5,027.6732
5,929.6694
6,989.2800
27
4,727.8868
5,624.7723
6,687.8054
7,946.7570
9,436.5280
28
6,194.5318
7,425.6994
8,895.7812
10,649.6543
12,740.3128
29
8,115.8366
9,802.9233
11,832.3890
14,271.5368
17,200.4222
30
10,632.7460
12,940.8587
15,738.0774
19,124.8593
23,221.5700
31
13,929.8972
17,082.9335
20,932.6429
25,628.3115
31,350.1195
32
18,249.1653
22,550.4722
27,841.4150
34,342.9374
42,323.6613
33
23,907.4066
29,707.6233
37,030.0820
46,020.5362
57,137.9428
34
31,319.7027
39,294.2628
49,251.0091
61,668.5185
77,137.2228
35
41,029.8105
51,869.4269
65,504.8420
82,636.8147
104,136.2507
36
53,750.0517
68,468.6435
87,122.4399
110,734.3317
140,584.9385
37
70,413.5677
90,379.6094
115,873.8451
148,385.0045
189,790.6670
38
92,242.7737
119,302.0844
154,113.2139
198,836.9061
256,218.4004
39
120,839.0336
157,479.7515
204,971.5745
266,442.4541
345,895.8406
40
158,300.1340
207,874.2719
272,613.1941
357,033.8885
466,960.3848
41
207,374.1756
274,395.0390
362,576.5482
478,426.4106
630,397.5195
42
271,661.1700
362,202.4514
482,227.8091
641,092.3902
851,037.6513
43
355,877.1327
478,108.2359
641,363.9861
859,064.8029
1,148,901.8293
44
466,200.0438
631,103.8714
853,015.1015
1,151,147.8359
1,551,018.4695
45
610,723.0574
833,058.1102
1,134,511.0850
1,542,539.1001
2,093,875.9338
46
800,048.2052
1,099,637.7055
1,508,900.7431
2,067,003.3942
2,826,733.5107
47
1,048,064.1488
1,451,522.7712
2,006,838.9883
2,769,785.5482
3,816,091.2394
48
1,372,965.0349
1,916,011.0580
2,669,096.8545
3,711,513.6346
5,151,724.1732
49
1,798,585.1957
2,529,135.5966
3,549,899.8165
4,973,429.2703
6,954,828.6337
50
2,356,147.6064
3,338,459.9875
4,721,367.7559
6,664,396.2223
9,389,019.6555
表八（36%~40%利率）
年金終值係數表（續表七）
利率
——
期數		36%37%38%39%40%
1
1.0000
1.0000
1.0000
1.0000
1.0000
2
2.3600
2.3700
2.3800
2.3900
2.4000
3
4.2096
4.2469
4.2844
4.3221
4.3600
4
6.7251
6.8183
6.9125
7.0077
7.1040
5
10.1461
10.3410
10.5392
10.7407
10.9456
6
14.7987
15.1672
15.5441
15.9296
16.3238
7
21.1262
21.7790
22.4509
23.1421
23.8534
8
29.7316
30.8373
31.9822
33.1676
34.3947
9
41.4350
43.2471
45.1354
47.1030
49.1526
10
57.3516
60.2485
63.2869
66.4731
69.1366
11
78.9982
83.5404
88.3359
93.3977
98.7391
12
108.4375
115.4503
122.9036
130.8227
139.2348
13
148.7498
159.1670
170.6070
182.8436
195.9287
14
202.9260
219.0588
236.4376
255.1526
275.3002
15
276.9793
301.1106
327.2839
355.6621
386.4202
16
377.6919
413.5215
452.6518
495.3704
541.9883
17
514.6610
567.5245
625.6595
689.5648
759.7837
18
700.9389
778.5085
864.4101
959.4951
1,064.6971
19
954.2769
1,067.5567
1,193.8859
1,334.6982
1,491.5760
20
1,298.8166
1,463.5527
1,648.5625
1,856.2305
2,089.2064
21
1,767.3906
2,006.0672
2,276.0162
2,581.1604
2,925.8889
22
2,404.6512
2,749.3120
3,141.9025
3,588.8129
4,097.2445
23
3,271.3256
3,767.5575
4,336.8254
4,989.4499
5,737.1423
24
4,450.0029
5,162.5537
5,985.8191
6,936.3354
8,032.9993
25
6,053.0039
7,073.6986
8,261.4304
9,642.5062
11,247.1990
26
8,233.0853
9,691.9671
11,401.7739
13,756.8227
16,575.8721
27
11,197.9960
13,278.9949
15,735.4480
19,123.0099
23,207.2736
28
15,230.2745
18,193.2230
21,715.9182
26,582.0101
32,491.2357
29
20,714.1734
24,925.7160
29,968.9671
36,950.0203
45,488.7826
30
28,172.2758
34,149.2304
41,358.1746
51,361.5545
63,685.3483
31
38,315.2951
46,785.4456
57,075.2810
69,562.9823
84,702.5132
32
52,109.8013
64,097.0605
78,764.8878
96,693.5454
118,584.5185
33
70,870.3298
87,813.9728
108,696.5451
134,405.0282
166,019.3260
34
96,384.6485
120,306.1428
150,002.2322
186,823.9891
232,428.0563
35
131,084.1219
164,820.4156
207,004.0805
259,686.3449
325,400.2789
36
178,275.4058
225,804.9694
285,666.6311
360,965.0194
455,561.3904
37
242,455.5519
309,353.8081
394 220.9509
501,742.3770
637,786.9466
38
329,740.5506
423,815.7171
544,025.9122
697,422.9040
892,902.7252
39
448,448.1488
580,628.5324
750 756.7589
969,418.8366
1,250,064.8153
40
609,890.4824
795,462.0894
1,036,045.3272
1,347,493.1829
1,750,091.7414
41
829,452.0560
1,089,784.0624
1,429,743.5516
1,873,016.5243
2,450,129.4381
42
1,128,055.7962
1,493,005.1656
1,973,047.1012
2,603,493.9687
3,430,182.2133
43
1,534,156.8828
2,045,418.0768
2,722,805.9996
3,618,857.6165
4,802,256.0986
44
2,086,454.3606
2,802,223.7653
3,757,473.2795
5,030,213.0870
6,723,159.5381
45
2,837,578.9304
3,839,047.5584
5,185,314.1257
6,991,997.1909
9,412,424.3532
46
3,859,108.3453
5,259,496.1551
7,155,734.4935
9,718,877.0953
13,177,395.0946
47
5,248,388.3496
7,205,510.7324
9,874,914.6010
13,509,240.1625
18,448,354.1324
48
7,137,809.1555
9,871,550.7034
13,627,383.1494
18,777,844.8258
25,827,696.7854
49
9,707,421.4515
13,524,025.4637
18,805,789.7462
26,101,205.3080
36,158,776.4996
50
13,202,094.1740
18,527,915.8853
25,951,990.8498
36,280,676.3781
50,622,288.0994
表九（41%~45%利率）
年金終值係數表（續表八）
利率
——
期數		41%42%43%44%45%
1
1.0000
1.0000
1.0000
1.0000
1.0000
2
2.4100
2.4200
2.4300
2.4400
2.4500
3
4.3981
4.4364
4.4749
4.5136
4.5525
4
7.2013
7.2997
7.3991
7.4996
7.6011
5
11.1539
11.3656
11.5807
11.7994
12.0216
6
16.7269
17.1391
17.5604
17.9911
18.4314
7
24.5850
25.3375
26.1114
26.9072
27.7255
8
35.6648
36.9793
38.3393
39.7464
41.2019
9
51.2874
53.5106
55.8252
58.2348
60.7428
10
73.3153
76.9850
80.8301
84.8582
89.0771
11
104.3745
110.3187
116.5870
123.1958
130.1618
12
148.1681
157.6525
167.7195
178.4019
189.7346
13
209.9170
224.8666
240.8388
257.8988
276.1151
14
296.9830
320.3106
345.3995
372.3742
401.3670
15
419.7460
455.8410
494.9213
537.2189
582.9821
16
592.8419
648.2942
708.7375
774.5952
846.3240
17
836.9070
921.5778
1,014.4947
1,116.4171
1 228.1699
18
1,181.0389
1,309.6404
1,451.7274
1,608.6406
1,781.8463
19
1,666.2649
1,860.6894
2,076.9701
2,317.4425
2,584.6771
20
2,350.4334
2,643.1789
2,971.0673
3,338.1172
3,748.7818
21
3,315.1112
3,754.3141
4,249.6262
4,807.8888
5,436.7336
22
4,675.3068
5,332.1260
6,077.9655
6,924.3598
7,884.2638
23
6,593.1826
7,572.6189
8,692.4906
9,972.0781
11,433.1824
24
9,297.3875
10,754.1189
12,431.2616
14,360.7925
16,579.1145
25
13,110.3164
15,271.8488
17,777.7041
20,680.5412
24,040.7161
26
18,486.5461
21,687.0253
25,423.1168
29,780.9794
34,860.0383
27
26,067.0300
30,796.5759
36,356.0571
42,885.6103
50,548.0556
28
36,755.5122
43,732.1378
51,990.1616
61,756.2789
73,295.6806
29
51,826.2723
62,100.6357
74,346.9311
88,930.0416
106,279.7368
30
73,076.0438
88,183.9027
106,317.1115
128,060.2599
154,106.6184
31
103,038.2218
125,222.1419
152,034.4694
184,407.7742
223,455.5967
32
145,284.8929
177,816.4415
217,410.2912
265,548.1949
324,011.6152
33
204,852.6989
252,500.3469
310,897.7165
382,390.4007
469,817.8421
34
288,843.3055
358,551.4925
444,584.7345
550,643.1770
681,236.8710
35
407,270.0607
509,144.1195
635,757.1704
792,927.1748
987,794.4630
36
574,251.7856
722,985.6496
909,133.7536
1,141,816.1318
1,432,302.9713
37
809,696.0177
1,026,640.6225
1,300,062.2677
1,644,216.2298
2,076,840.3084
38
1,141,672.3850
1,457,830.6839
1,859,090.0428
2,367,672.3709
3,011,419.4472
39
1,609,759.0628
2,070,120.5711
2,658,499.7613
3,409,449.2140
4,366,559.1985
40
2,269,761.2786
2,939,572.2110
3,801,655.6586
4,909,607.8682
6,331,511.8378
41
3,200,364.4028
4,174,193.5396
5,436,368.5918
7,069,836.3302
9,180,693.1648
42
4,512,514.8080
5,927,355.8263
7,774,008.0863
10,180,565.3155
13,312,006.0890
43
6,362,646.8793
8,416,846.2733
11,116,832.5634
14,660,015.0543
19,302,409.8290
44
8,971,333.0997
11,951,922.7081
15,897,071.5656
21,110,422.6782
27,988,495.2521
45
12,649,580.6706
16,971,731.2455
22,732,813.3388
30,399,009.6566
40,583,319.1155
46
17,835,909.7456
24,099,859.3686
32,507,924.0745
43,774,574.9056
58,845,813.7175
47
25,148,633.7413
34,221,801.3034
46,486,332.4266
63,035,388.8641
85,326,430.8904
48
35,459,574.5752
48,594,958.8508
66,475,456.3700
90,770,960.9643
123,723,325.7910
49
49,998,001.1511
69,004,842.5681
95,059,903.6091
130,710,184.7885
179,398,823.3970
50
70,497,182.6230
97,986,877.4468
135,935,663.1610
188,222,667.0955
260,128,294.9257
表十（46%~50%利率）
年金終值係數表（續表九）
利率
——
期數		46%47%48%49%50%
1
1.0000
1.0000
1.0000
1.0000
1.0000
2
2.4600
2.4700
2.4800
2.4900
2.5000
3
4.5916
4.6309
4.6704
4.7101
4.7500
4
7.7037
7.8074
7.9122
8.0180
8.1250
5
12.2475
12.4769
12.7100
12.9469
13.1875
6
18.8813
19.3411
19.8109
20.2909
20.7813
7
28.5667
29.4314
30.3201
31.2334
32.1719
8
42.7073
44.2641
45.8737
47.5378
49.2578
9
63.3527
66.0682
68.8931
71.8313
74.8867
10
93.4950
98.1203
102.9618
108.0286
113.3301
11
137.5027
145.2368
153.3835
161.9626
170.9951
12
201.7539
214.4981
228.0075
242.3243
257.4927
13
295.5607
316.3122
338.4511
362.0631
387.2390
14
432.5186
465.9790
501.9077
540.4741
581.8585
15
632.4771
685.9891
743.8233
806.3064
873.7878
16
924.4166
1,009.4040
1,101.8585
1,202.3965
1,311.6817
17
1 350.6483
1,484.8239
1,631.7506
1,792.5708
1,968.5225
18
1,972.9465
2,183.6912
2,415.9910
2,671.9305
2,953.7838
19
2,881.5019
3,211.0261
3,576.6666
3,982.1765
4,431.6756
20
4,207.9927
4,721.2083
5,294.4666
5,934.4430
6,648.5135
21
6,144.6694
6,941.1762
7,836.8106
8,843.3201
9,973.7702
22
8,972.2173
10,204.5290
11,599.4796
13,177.5469
14,961.6553
23
13,100.4372
15 001.6577
17,168.2299
19,635.5449
22,443.4829
24
19,127.6383
22,053.4368
25,409.9802
29,257.9619
33,666.2244
25
27,927.3519
32,419.5520
37,607.7707
43,595.3632
50,500.3366
26
40,774.9338
47,657.7414
55,660.5006
64,958.0912
75,751.5049
27
59,532.4034
70,057.8800
82,378.5409
96,788.5559
113,628.2573
28
86,918.3090
102,986.0836
121,921.2405
144,215.9482
170,443.3860
29
126,901.7311
151,390.5428
180,444.4359
214,882.7628
255,666.0790
30
185,277.5273
222,545.0980
267,058.7652
320,176.3167
383,500.1185
31
270,506.1900
327,142.2940
395,247.9724
477,063.7118
575,251.1777
32
394,940.0373
480,900.1722
584,967.9992
710,825.9306
862,877.7665
33
576,613.4545
706,924.2531
865,753.6388
1,059,131.6366
1,294,317.6498
34
841,856.6436
1,039,179.6520
1,281,316.3854
1,578,107.1385
1,941,477.4747
35
1,229,111.6996
1,527,595.0884
1,896,349.2504
2,351,380.6364
2,912,217.2121
36
1,794,504.0815
2,245,565.7801
2,806,597.8906
3,503,558.1483
4,368,326.8181
37
2,619,976.9589
3,300,982.6967
4,153,765.8781
5,220,302.6409
6,552,491.2272
38
3,825,167.3601
4,852,445.5641
6,147,574.4996
7,778,251.9349
9,828,737.8408
39
5,584,745.3457
7,133,095.9792
9,098,411.2594
11,589,596.3831
14,743,107.7613
40
8,153,729.2047
10,485,652.0895
13,465,649.6639
17,268,499.6108
22,114,662.6419
41
11,904,445.6389
15,413,909.5716
19,929,162.5026
25,730,065.4200
33,171,994.9628
42
17,380,491.6328
22,658,448.0702
29,495,161.5039
38,337,798.4758
49,757,993.4442
43
25,375,518.7838
33,307,919.6631
43,652,840.0257
57,123,320.7290
74,636,991.1663
44
37,048,258.4244
48,962,642.9048
64,606,204.2381
85,113,748.8862
111,955,487.7495
45
54,090,458.2996
71,975,086.0702
95,617,183.2724
126,819,486.8405
167,933,232.6243
46
78,972,070.1174
105,803,377.5231
141,513,432.2431
188,961,036.3923
251,899,849.9364
47
115,299,223.3714
155,530,965.9590
209,439,880.7198
281,551,945.2245
377,849,775.9046
48
168,336,867.1223
228,630,520.9598
309,971,024.4653
419,512,399.3845
566,774,664.8569
49
245,771,826.9985
336,086,866.8109
458,757,117.2087
625,073,476.0830
850,161,998.2854
50
358,826,868.4178
494,047,695.2120
678,960,534.4689
931,359,480.3636
1,275,242,998.4281

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