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Calculation of a pension by a lump sum payment

Life annuity - a life-long pension in the name of one person

An annuity for life is a monthly payment, a guaranteed, life-long payment in the name of one person.

Often considerable funds become available upon going into retirement or before retirement age . These may be a payout of capital life assurances, sales, sales revenue from no longer suitable real estate or also from legacies.
This money should then usually be a financial security for old-age. However, one does not know how long this period of old age will be. It is therefore possible, if the danger of running out of money some day is to be avoided, to only use the revenue for subsistence and consumption At this point insurance companies offer a life-long pension for a lump sum payment. As capital is thus used up, annuitisation of capital is spoken of. The advantage for those eligible for pension is a relatively high payment up to the end of his/her life.

In principle this is a loan that the eligible for pension extends to an insurance company. The insurance company calculates the pension in a manner by which the loan would be redeemed within the life expectancy of the eligible for a pension.

Reverse mortgage:
The capital may also consist of the value of real estate. In such cases the sale on an annuity basis is spoken of. When a right of abode has been drawn up, a fictive rental payment has to be deducted from the annuity for life. The circumstance must also be considered that the purchaser may not dispose freely of the real estate for an uncertain period of time. The annuity for life should therefore be fixed lower.

The person--> Starting basis for an annuity for life

Name of the calculation:
Gender:
Date of birth:
individual life expectancy*: Years

*if you do not fill in this field, the remaining life expectancy of the Federal Statistical Office of Germany (2004) is used.

The amount of annuity for life--> Payment data

Annuitisation capital:
Nominal interest rate: %
Date of the lump sum payment*:
Start of annuity payment**:

*the beginning of the contract and decisive for the calculation of life expectancy
**Annuity is paid in arrears. First payment date is therefore the following month.

The amount of annuity for life--> Result

Annuity for life for: Pension for
Birthday: 1954-1-5
Gender:male
Payment or transfer date: 2012-10-1
Start of pension payment: 2012-10-1
Time between payments and beginning of pension: 0.00 Years
Amount of lump sum payment: 100000.00 $
Assumed interest rate level: 2.75 %
Annuitisation capital at the beginning: 100000.00 $
Age upon start of contract (payment date): 58.74 Years
Statistical life expectancy:77.82 Years
Age at start of pension:58.74 Years
Average duration of payment:19.08 Years
Pension without capital erosion:226.33 $

Life-long pension with capital erosion:

560.11$

Any warranty for the correctness of the numbers is excluded.

The annuity for life calculated here is to be seen as the mathematically correct value. However, in the calculation no risk premium, no costs and no profit have been considered for the insurer. In addition, you should keep in mind, that the life expectancy has been constantly increased in the past decades and there are groups of persons with considerably higher life expectancies than the average of the population. The insurers therefore work with differentiated statistical data, which they collect in their own databases. or purchase from special companies .

The calculation basis--> exemplary loan redemption schedule

No. Date Annuitisation capital Pension payment thereof interest capital erosion remaining capital
1. 2012-11-01100000.00560.11   226.33 333.79 99666.21
2. 2012-12-0199666.21560.11   225.57 334.54 99331.67
3. 2013-01-0199331.67560.11   224.82 335.30 98996.37
4. 2013-02-0198996.37560.11   224.06 336.06 98660.32
5. 2013-03-0198660.32560.11   223.30 336.82 98323.50
6. 2013-04-0198323.50560.11   222.53 337.58 97985.92
7. 2013-05-0197985.92560.11   221.77 338.34 97647.58
8. 2013-06-0197647.58560.11   221.00 339.11 97308.47
9. 2013-07-0197308.47560.11   220.24 339.88 96968.59
10. 2013-08-0196968.59560.11   219.47 340.65 96627.94
11. 2013-09-0196627.94560.11   218.70 341.42 96286.52
12. 2013-10-0196286.52560.11   217.92 342.19 95944.33
13. 2013-11-0195944.33560.11   217.15 342.96 95601.37
14. 2013-12-0195601.37560.11   216.37 343.74 95257.63
15. 2014-01-0195257.63560.11   215.59 344.52 94913.11
16. 2014-02-0194913.11560.11   214.81 345.30 94567.81
17. 2014-03-0194567.81560.11   214.03 346.08 94221.73
18. 2014-04-0194221.73560.11   213.25 346.86 93874.87
19. 2014-05-0193874.87560.11   212.47 347.65 93527.22
20. 2014-06-0193527.22560.11   211.68 348.44 93178.78
21. 2014-07-0193178.78560.11   210.89 349.22 92829.56
22. 2014-08-0192829.56560.11   210.10 350.01 92479.54
23. 2014-09-0192479.54560.11   209.31 350.81 92128.74
24. 2014-10-0192128.74560.11   208.51 351.60 91777.14
25. 2014-11-0191777.14560.11   207.72 352.40 91424.74
26. 2014-12-0191424.74560.11   206.92 353.19 91071.55
27. 2015-01-0191071.55560.11   206.12 353.99 90717.55
28. 2015-02-0190717.55560.11   205.32 354.79 90362.76
29. 2015-03-0190362.76560.11   204.52 355.60 90007.16
30. 2015-04-0190007.16560.11   203.71 356.40 89650.76
31. 2015-05-0189650.76560.11   202.90 357.21 89293.55
32. 2015-06-0189293.55560.11   202.10 358.02 88935.53
33. 2015-07-0188935.53560.11   201.29 358.83 88576.71
34. 2015-08-0188576.71560.11   200.47 359.64 88217.07
35. 2015-09-0188217.07560.11   199.66 360.45 87856.61
36. 2015-10-0187856.61560.11   198.84 361.27 87495.34
37. 2015-11-0187495.34560.11   198.03 362.09 87133.26
38. 2015-12-0187133.26560.11   197.21 362.91 86770.35
39. 2016-01-0186770.35560.11   196.39 363.73 86406.62
40. 2016-02-0186406.62560.11   195.56 364.55 86042.07
41. 2016-03-0186042.07560.11   194.74 365.38 85676.69
42. 2016-04-0185676.69560.11   193.91 366.20 85310.49
43. 2016-05-0185310.49560.11   193.08 367.03 84943.46
44. 2016-06-0184943.46560.11   192.25 367.86 84575.59
45. 2016-07-0184575.59560.11   191.42 368.70 84206.90
46. 2016-08-0184206.90560.11   190.58 369.53 83837.37
47. 2016-09-0183837.37560.11   189.75 370.37 83467.00
48. 2016-10-0183467.00560.11   188.91 371.20 83095.80
49. 2016-11-0183095.80560.11   188.07 372.04 82723.75
50. 2016-12-0182723.75560.11   187.23 372.89 82350.87
51. 2017-01-0182350.87560.11   186.38 373.73 81977.14
52. 2017-02-0181977.14560.11   185.54 374.58 81602.56
53. 2017-03-0181602.56560.11   184.69 375.42 81227.14
54. 2017-04-0181227.14560.11   183.84 376.27 80850.86
55. 2017-05-0180850.86560.11   182.99 377.13 80473.74
56. 2017-06-0180473.74560.11   182.13 377.98 80095.76
57. 2017-07-0180095.76560.11   181.28 378.83 79716.92
58. 2017-08-0179716.92560.11   180.42 379.69 79337.23
59. 2017-09-0179337.23560.11   179.56 380.55 78956.68
60. 2017-10-0178956.68560.11   178.70 381.41 78575.27
61. 2017-11-0178575.27560.11   177.84 382.28 78192.99
62. 2017-12-0178192.99560.11   176.97 383.14 77809.85
63. 2018-01-0177809.85560.11   176.11 384.01 77425.84
64. 2018-02-0177425.84560.11   175.24 384.88 77040.96
65. 2018-03-0177040.96560.11   174.37 385.75 76655.22
66. 2018-04-0176655.22560.11   173.49 386.62 76268.59
67. 2018-05-0176268.59560.11   172.62 387.50 75881.10
68. 2018-06-0175881.10560.11   171.74 388.37 75492.72
69. 2018-07-0175492.72560.11   170.86 389.25 75103.47
70. 2018-08-0175103.47560.11   169.98 390.13 74713.34
71. 2018-09-0174713.34560.11   169.10 391.02 74322.32
72. 2018-10-0174322.32560.11   168.21 391.90 73930.42
73. 2018-11-0173930.42560.11   167.33 392.79 73537.63
74. 2018-12-0173537.63560.11   166.44 393.68 73143.95
75. 2019-01-0173143.95560.11   165.55 394.57 72749.39
76. 2019-02-0172749.39560.11   164.65 395.46 72353.92
77. 2019-03-0172353.92560.11   163.76 396.36 71957.57
78. 2019-04-0171957.57560.11   162.86 397.25 71560.31
79. 2019-05-0171560.31560.11   161.96 398.15 71162.16
80. 2019-06-0171162.16560.11   161.06 399.05 70763.11
81. 2019-07-0170763.11560.11   160.16 399.96 70363.15
82. 2019-08-0170363.15560.11   159.25 400.86 69962.29
83. 2019-09-0169962.29560.11   158.34 401.77 69560.52
84. 2019-10-0169560.52560.11   157.43 402.68 69157.84
85. 2019-11-0169157.84560.11   156.52 403.59 68754.25
86. 2019-12-0168754.25560.11   155.61 404.50 68349.75
87. 2020-01-0168349.75560.11   154.69 405.42 67944.33
88. 2020-02-0167944.33560.11   153.78 406.34 67537.99
89. 2020-03-0167537.99560.11   152.86 407.26 67130.74
90. 2020-04-0167130.74560.11   151.94 408.18 66722.56
91. 2020-05-0166722.56560.11   151.01 409.10 66313.46
92. 2020-06-0166313.46560.11   150.09 410.03 65903.43
93. 2020-07-0165903.43560.11   149.16 410.96 65492.47
94. 2020-08-0165492.47560.11   148.23 411.89 65080.59
95. 2020-09-0165080.59560.11   147.30 412.82 64667.77
96. 2020-10-0164667.77560.11   146.36 413.75 64254.02
97. 2020-11-0164254.02560.11   145.42 414.69 63839.33
98. 2020-12-0163839.33560.11   144.49 415.63 63423.70
99. 2021-01-0163423.70560.11   143.55 416.57 63007.13
100. 2021-02-0163007.13560.11   142.60 417.51 62589.62
101. 2021-03-0162589.62560.11   141.66 418.46 62171.16
102. 2021-04-0162171.16560.11   140.71 419.40 61751.76
103. 2021-05-0161751.76560.11   139.76 420.35 61331.41
104. 2021-06-0161331.41560.11   138.81 421.30 60910.11
105. 2021-07-0160910.11560.11   137.86 422.26 60487.85
106. 2021-08-0160487.85560.11   136.90 423.21 60064.64
107. 2021-09-0160064.64560.11   135.94 424.17 59640.47
108. 2021-10-0159640.47560.11   134.98 425.13 59215.33
109. 2021-11-0159215.33560.11   134.02 426.09 58789.24
110. 2021-12-0158789.24560.11   133.06 427.06 58362.18
111. 2022-01-0158362.18560.11   132.09 428.02 57934.16
112. 2022-02-0157934.16560.11   131.12 428.99 57505.17
113. 2022-03-0157505.17560.11   130.15 429.96 57075.21
114. 2022-04-0157075.21560.11   129.18 430.94 56644.27
115. 2022-05-0156644.27560.11   128.20 431.91 56212.36
116. 2022-06-0156212.36560.11   127.22 432.89 55779.47
117. 2022-07-0155779.47560.11   126.24 433.87 55345.60
118. 2022-08-0155345.60560.11   125.26 434.85 54910.75
119. 2022-09-0154910.75560.11   124.28 435.84 54474.91
120. 2022-10-0154474.91560.11   123.29 436.82 54038.09
121. 2022-11-0154038.09560.11   122.30 437.81 53600.28
122. 2022-12-0153600.28560.11   121.31 438.80 53161.48
123. 2023-01-0153161.48560.11   120.32 439.79 52721.68
124. 2023-02-0152721.68560.11   119.32 440.79 52280.89
125. 2023-03-0152280.89560.11   118.33 441.79 51839.11
126. 2023-04-0151839.11560.11   117.33 442.79 51396.32
127. 2023-05-0151396.32560.11   116.32 443.79 50952.53
128. 2023-06-0150952.53560.11   115.32 444.79 50507.74
129. 2023-07-0150507.74560.11   114.31 445.80 50061.94
130. 2023-08-0150061.94560.11   113.30 446.81 49615.13
131. 2023-09-0149615.13560.11   112.29 447.82 49167.31
132. 2023-10-0149167.31560.11   111.28 448.83 48718.47
133. 2023-11-0148718.47560.11   110.26 449.85 48268.62
134. 2023-12-0148268.62560.11   109.25 450.87 47817.75
135. 2024-01-0147817.75560.11   108.22 451.89 47365.86
136. 2024-02-0147365.86560.11   107.20 452.91 46912.95
137. 2024-03-0146912.95560.11   106.18 453.94 46459.02
138. 2024-04-0146459.02560.11   105.15 454.96 46004.05
139. 2024-05-0146004.05560.11   104.12 455.99 45548.06
140. 2024-06-0145548.06560.11   103.09 457.03 45091.03
141. 2024-07-0145091.03560.11   102.05 458.06 44632.97
142. 2024-08-0144632.97560.11   101.02 459.10 44173.88
143. 2024-09-0144173.88560.11   99.98 460.14 43713.74
144. 2024-10-0143713.74560.11   98.94 461.18 43252.56
145. 2024-11-0143252.56560.11   97.89 462.22 42790.34
146. 2024-12-0142790.34560.11   96.85 463.27 42327.08
147. 2025-01-0142327.08560.11   95.80 464.32 41862.76
148. 2025-02-0141862.76560.11   94.75 465.37 41397.39
149. 2025-03-0141397.39560.11   93.69 466.42 40930.97
150. 2025-04-0140930.97560.11   92.64 467.48 40463.50
151. 2025-05-0140463.50560.11   91.58 468.53 39994.97
152. 2025-06-0139994.97560.11   90.52 469.59 39525.37
153. 2025-07-0139525.37560.11   89.46 470.66 39054.71
154. 2025-08-0139054.71560.11   88.39 471.72 38582.99
155. 2025-09-0138582.99560.11   87.32 472.79 38110.20
156. 2025-10-0138110.20560.11   86.25 473.86 37636.34
157. 2025-11-0137636.34560.11   85.18 474.93 37161.41
158. 2025-12-0137161.41560.11   84.11 476.01 36685.40
159. 2026-01-0136685.40560.11   83.03 477.08 36208.32
160. 2026-02-0136208.32560.11   81.95 478.16 35730.16
161. 2026-03-0135730.16560.11   80.87 479.25 35250.91
162. 2026-04-0135250.91560.11   79.78 480.33 34770.58
163. 2026-05-0134770.58560.11   78.70 481.42 34289.16
164. 2026-06-0134289.16560.11   77.61 482.51 33806.65
165. 2026-07-0133806.65560.11   76.51 483.60 33323.05
166. 2026-08-0133323.05560.11   75.42 484.69 32838.36
167. 2026-09-0132838.36560.11   74.32 485.79 32352.57
168. 2026-10-0132352.57560.11   73.22 486.89 31865.68
169. 2026-11-0131865.68560.11   72.12 487.99 31377.68
170. 2026-12-0131377.68560.11   71.02 489.10 30888.59
171. 2027-01-0130888.59560.11   69.91 490.20 30398.38
172. 2027-02-0130398.38560.11   68.80 491.31 29907.07
173. 2027-03-0129907.07560.11   67.69 492.43 29414.64
174. 2027-04-0129414.64560.11   66.57 493.54 28921.10
175. 2027-05-0128921.10560.11   65.46 494.66 28426.45
176. 2027-06-0128426.45560.11   64.34 495.78 27930.67
177. 2027-07-0127930.67560.11   63.21 496.90 27433.77
178. 2027-08-0127433.77560.11   62.09 498.02 26935.75
179. 2027-09-0126935.75560.11   60.96 499.15 26436.60
180. 2027-10-0126436.60560.11   59.83 500.28 25936.32
181. 2027-11-0125936.32560.11   58.70 501.41 25434.90
182. 2027-12-0125434.90560.11   57.57 502.55 24932.36
183. 2028-01-0124932.36560.11   56.43 503.68 24428.67
184. 2028-02-0124428.67560.11   55.29 504.82 23923.85
185. 2028-03-0123923.85560.11   54.15 505.97 23417.88
186. 2028-04-0123417.88560.11   53.00 507.11 22910.77
187. 2028-05-0122910.77560.11   51.85 508.26 22402.51
188. 2028-06-0122402.51560.11   50.70 509.41 21893.10
189. 2028-07-0121893.10560.11   49.55 510.56 21382.53
190. 2028-08-0121382.53560.11   48.39 511.72 20870.81
191. 2028-09-0120870.81560.11   47.24 512.88 20357.94
192. 2028-10-0120357.94560.11   46.08 514.04 19843.90
193. 2028-11-0119843.90560.11   44.91 515.20 19328.70
194. 2028-12-0119328.70560.11   43.75 516.37 18812.33
195. 2029-01-0118812.33560.11   42.58 517.54 18294.79
196. 2029-02-0118294.79560.11   41.41 518.71 17776.09
197. 2029-03-0117776.09560.11   40.23 519.88 17256.21
198. 2029-04-0117256.21560.11   39.06 521.06 16735.15
199. 2029-05-0116735.15560.11   37.88 522.24 16212.91
200. 2029-06-0116212.91560.11   36.69 523.42 15689.49
201. 2029-07-0115689.49560.11   35.51 524.60 15164.89
202. 2029-08-0115164.89560.11   34.32 525.79 14639.10
203. 2029-09-0114639.10560.11   33.13 526.98 14112.11
204. 2029-10-0114112.11560.11   31.94 528.17 13583.94
205. 2029-11-0113583.94560.11   30.74 529.37 13054.57
206. 2029-12-0113054.57560.11   29.55 530.57 12524.00
207. 2030-01-0112524.00560.11   28.35 531.77 11992.24
208. 2030-02-0111992.24560.11   27.14 532.97 11459.26
209. 2030-03-0111459.26560.11   25.94 534.18 10925.09
210. 2030-04-0110925.09560.11   24.73 535.39 10389.70
211. 2030-05-0110389.70560.11   23.51 536.60 9853.10
212. 2030-06-019853.10560.11   22.30 537.81 9315.29
213. 2030-07-019315.29560.11   21.08 539.03 8776.26
214. 2030-08-018776.26560.11   19.86 540.25 8236.01
215. 2030-09-018236.01560.11   18.64 541.47 7694.53
216. 2030-10-017694.53560.11   17.41 542.70 7151.83
217. 2030-11-017151.83560.11   16.19 543.93 6607.91
218. 2030-12-016607.91560.11   14.96 545.16 6062.75
219. 2031-01-016062.75560.11   13.72 546.39 5516.36
220. 2031-02-015516.36560.11   12.49 547.63 4968.73
221. 2031-03-014968.73560.11   11.25 548.87 4419.86
222. 2031-04-014419.86560.11   10.00 550.11 3869.75
223. 2031-05-013869.75560.11   8.76 551.36 3318.39
224. 2031-06-013318.39560.11   7.51 552.60 2765.79
225. 2031-07-012765.79560.11   6.26 553.85 2211.94
226. 2031-08-012211.94560.11   5.01 555.11 1656.83
227. 2031-09-011656.83560.11   3.75 556.36 1100.47
228. 2031-10-011100.47560.11   2.49 557.62 542.84
229. 2031-11-01542.84560.11   1.23 542.84 0.00
230. 2031-12-01 - 560.11   - - -
231. 2032-01-01 - 560.11   - - -
... ... - 560.11   - - -
A life-long annuity is paid to the person entitled to the benefit. The interest is calculated as effective interest yield and not as nominal interest as in a loan redemption schedule for a mortgage.


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