## FLEXIBLE RETIREMENT FUND TO ACCUMULATE SAVINGS AND PAY COSTS ASSOCIATED WITH EARLY AND LATE RETIREMENT

#### Page X

In this Example a person age 60 retires at age 60 upon receiving one times salary of \$85000. The savings (costs) year by year are calculated. At the same time a person age 65 continues on at a salary of 80% of their salary of \$90,000 until age 69. The costs (savings) year by year are recorded. A Fund is set up. Into this fund savings incurred are deposited and costs are withdrawn. If necessary funds are borrowed so that the fund can have a negative balance. Assume the fund earns or costs 5% per year. In this example after approx 20 years there is a minimal positive or negative balance in the fund. The early and late retirements have balanced one another and no net costs have incurred.

The same can be done in each case of early or late retirement. After 20 years (or some other agreed time) the individual is removed from the fund. The fund is allowed to range, in total, between say minus and plus a \$million . Every year the fund is examined, just as a pension fund is. If there are major deficits or savings adjustments are required, perhaps negotiations to modify the early or late retirement rules are necessary.

The example here is but one of a large number of studies done.

```
Page X                                                                                                   ***
Morton Abramson    Maths dept.                      1 year salary bonus paid at 60                       ***
80% of Salary paid at 65                             ***
SAVINGS WHEN RETIREMENT IS AT AGE 60                                                                     ***PERSON AGE 65 RETIRES AT AGE 69
yearly                                   yearly                   ***                                          yearly                                      yearly
% increase                               % increase                 ***                                        % increase                                  % increase
EXAMPLE:                            to person 60            starting           to person                 ***EXAMPLE:                         to person 65                    starting           to person
salary at 60           to age 65           salary at 35          age 35     interest rate ***               salary at 65             to age 69              salary at 35           age 35      interest rate
When                X =                  r =                   Y=                 s =           i =      ***When               X =                     r =                      Y=                 s =             i =
\$85,000                2.5%                \$45,000              2.5%            5%      ***                 \$90,000                   0.0%                  \$45,000               2.5%            5%
***
THEN   person age 60 continues to 65 and         person age 60 retires at 60 and is                   ***  THEN   person age 65 continues to 69 and               person age 65 retires at age 65
is then replaced by person age 35         replaced by person age 35                            ***         is then replaced by person age 35               and is replaced by person age 35
***
person                 has                 person               has                    ***                  person                   has                    person               has
age                salary                 age               salary                   ***                   age                    salary                   age                salary                      Flexible
number                               paid at                                  paid at        yearly    *** number                                  paid at                                     paid at         yearly      Retirement
of years                            end of year                              end of year     savings    ***of years                               end of year                                 end of year        cost          Fund
0               60                                60 is replaced by 35     \$85,000       (\$85,000)   ***    0               65                                     65 is replaced by 35        \$0                        (\$85,000)
1               61                      \$85,000            36              \$45,000        \$40,000    ***    1               66                   \$72,000                    36               \$45,000        \$27,000      (\$76,250)
2               62                      \$87,125            37              \$46,125        \$41,000    ***    2               67                   \$72,000                    37               \$46,125        \$25,875      (\$64,938)
3               63                      \$89,303            38              \$47,278        \$42,025    ***    3               68                   \$72,000                    38               \$47,278        \$24,722      (\$50,881)
4               64                      \$91,536            39              \$48,460        \$43,076    ***    4      69 is replaced by 35          \$72,000                    39               \$48,460        \$23,540      (\$33,890)
5       65 is replaced by 35            \$93,824            40              \$49,672        \$44,153    ***    5               36                   \$45,000                    40               \$49,672        (\$4,672)      \$13,240
6               36                      \$45,000            41              \$50,913        (\$5,913)   ***    6               37                   \$46,125                    41               \$50,913        (\$4,788)      \$12,777
7               37                      \$46,125            42              \$52,186        (\$6,061)   ***    7               38                   \$47,278                    42               \$52,186        (\$4,908)      \$12,263
8               38                      \$47,278            43              \$53,491        (\$6,213)   ***    8               39                   \$48,460                    43               \$53,491        (\$5,031)      \$11,694
9               39                      \$48,460            44              \$54,828        (\$6,368)   ***    9               40                   \$49,672                    44               \$54,828        (\$5,157)      \$11,067
10              40                      \$49,672            45              \$56,199        (\$6,527)   ***   10               41                   \$50,913                    45               \$56,199        (\$5,285)      \$10,379
11              41                      \$50,913            46              \$57,604        (\$6,690)   ***   11               42                   \$52,186                    46               \$57,604        (\$5,418)      \$9,625
12              42                      \$52,186            47              \$59,044        (\$6,858)   ***   12               43                   \$53,491                    47               \$59,044        (\$5,553)      \$8,801
13              43                      \$53,491            48              \$60,520        (\$7,029)   ***   13               44                   \$54,828                    48               \$60,520        (\$5,692)      \$7,904
14              44                      \$54,828            49              \$62,033        (\$7,205)   ***   14               45                   \$56,199                    49               \$62,033        (\$5,834)      \$6,929
15              45                      \$56,199            50              \$63,584        (\$7,385)   ***   15               46                   \$57,604                    50               \$63,584        (\$5,980)      \$5,870
16              46                      \$57,604            51              \$65,173        (\$7,570)   ***   16               47                   \$59,044                    51               \$65,173        (\$6,130)      \$4,724
17              47                      \$59,044            52              \$66,803        (\$7,759)   ***   17               48                   \$60,520                    52               \$66,803        (\$6,283)      \$3,484
18              48                      \$60,520            53              \$68,473        (\$7,953)   ***   18               49                   \$62,033                    53               \$68,473        (\$6,440)      \$2,145
19              49                      \$62,033            54              \$70,185        (\$8,152)   ***   19               50                   \$63,584                    54               \$70,185        (\$6,601)       \$701
20              50                      \$63,584            55              \$71,939        (\$8,355)   ***   20               51                   \$65,173                    55               \$71,939        (\$6,766)       (\$853)
21              51                      \$65,173            56              \$73,738        (\$8,564)   ***   21               52                   \$66,803                    56               \$73,738        (\$6,935)      (\$2,525)
22              52                      \$66,803            57              \$75,581        (\$8,778)   ***   22               53                   \$68,473                    57               \$75,581        (\$7,108)      (\$4,322)
23              53                      \$68,473            58              \$77,471        (\$8,998)   ***   23               54                   \$70,185                    58               \$77,471        (\$7,286)      (\$6,250)
24              54                      \$70,185            59              \$79,407        (\$9,223)   ***   24               55                   \$71,939                    59               \$79,407        (\$7,468)      (\$8,317)
25              55                      \$71,939            60              \$81,393        (\$9,453)   ***   25               56                   \$73,738                    60               \$81,393        (\$7,655)     (\$10,531)
26              56                      \$73,738            61              \$83,427        (\$9,690)   ***   26               57                   \$75,581                    61               \$83,427        (\$7,846)     (\$12,901)
27              57                      \$75,581            62              \$85,513        (\$9,932)   ***   27               58                   \$77,471                    62               \$85,513        (\$8,042)     (\$15,436)
28              58                      \$77,471            63              \$87,651       (\$10,180)   ***   28               59                   \$79,407                    63               \$87,651        (\$8,244)     (\$18,144)
29              59                      \$79,407            64              \$89,842       (\$10,435)   ***   29               60                   \$81,393                    64               \$89,842        (\$8,450)     (\$21,036)
30              60                      \$81,393   65 is replaced by 35     \$92,088       (\$10,696)   ***   30               61                   \$83,427           65 is replaced by 35      \$92,088        (\$8,661)     (\$24,123)
31              61                      \$83,427            36              \$45,000        \$38,427    ***   31               62                   \$85,513                    36               \$45,000        \$40,513      (\$27,415)
32              62                      \$85,513            37              \$46,125        \$39,388    ***   32               63                   \$87,651                    37               \$46,125        \$41,526      (\$30,924)
33              63                      \$87,651            38              \$47,278        \$40,373    ***   33               64                   \$89,842                    38               \$47,278        \$42,564      (\$34,661)
34              64                      \$89,842            39              \$48,460        \$41,382    ***   34      65 is replaced by 35          \$92,088                    39               \$48,460        \$43,628      (\$38,640)
35      65 is replaced by 35            \$92,088            40              \$49,672        \$42,417    ***   35               36                   \$45,000                    40               \$49,672        (\$4,672)      \$6,516
36              36                      \$45,000            41              \$50,913        (\$5,913)   ***   36               37                   \$46,125                    41               \$50,913        (\$4,788)      \$5,717
37              37                      \$46,125            42              \$52,186        (\$6,061)   ***   37               38                   \$47,278                    42               \$52,186        (\$4,908)      \$4,850
38              38                      \$47,278            43              \$53,491        (\$6,213)   ***   38               39                   \$48,460                    43               \$53,491        (\$5,031)      \$3,910
39              39                      \$48,460            44              \$54,828        (\$6,368)   ***   39               40                   \$49,672                    44               \$54,828        (\$5,157)      \$2,894
40              40                      \$49,672            45              \$56,199        (\$6,527)   ***   40               41                   \$50,913                    45               \$56,199        (\$5,285)      \$1,797
41              41                      \$50,913            46              \$57,604        (\$6,690)   ***   41               42                   \$52,186                    46               \$57,604        (\$5,418)       \$614
42              42                      \$52,186            47              \$59,044        (\$6,858)   ***   42               43                   \$53,491                    47               \$59,044        (\$5,553)       (\$660)
43              43                      \$53,491            48              \$60,520        (\$7,029)   ***   43               44                   \$54,828                    48               \$60,520        (\$5,692)      (\$2,030)
44              44                      \$54,828            49              \$62,033        (\$7,205)   ***   44               45                   \$56,199                    49               \$62,033        (\$5,834)      (\$3,502)
45              45                      \$56,199            50              \$63,584        (\$7,385)   ***   45               46                   \$57,604                    50               \$63,584        (\$5,980)      (\$5,082)
46              46                      \$57,604            51              \$65,173        (\$7,570)   ***   46               47                   \$59,044                    51               \$65,173        (\$6,130)      (\$6,776)
47              47                      \$59,044            52              \$66,803        (\$7,759)   ***   47               48                   \$60,520                    52               \$66,803        (\$6,283)      (\$8,591)
48              48                      \$60,520            53              \$68,473        (\$7,953)   ***   48               49                   \$62,033                    53               \$68,473        (\$6,440)     (\$10,534)
49              49                      \$62,033            54              \$70,185        (\$8,152)   ***   49               50                   \$63,584                    54               \$70,185        (\$6,601)     (\$12,611)
50              50                      \$63,584            55              \$71,939        (\$8,355)   ***   50               51                   \$65,173                    55               \$71,939        (\$6,766)     (\$14,832)
51              51                      \$65,173            56              \$73,738        (\$8,564)   ***   51               52                   \$66,803                    56               \$73,738        (\$6,935)     (\$17,203)
52              52                      \$66,803            57              \$75,581        (\$8,778)   ***   52               53                   \$68,473                    57               \$75,581        (\$7,108)     (\$19,733)
53              53                      \$68,473            58              \$77,471        (\$8,998)   ***   53               54                   \$70,185                    58               \$77,471        (\$7,286)     (\$22,431)
54              54                      \$70,185            59              \$79,407        (\$9,223)   ***   54               55                   \$71,939                    59               \$79,407        (\$7,468)     (\$25,307)
55              55                      \$71,939            60              \$81,393        (\$9,453)   ***   55               56                   \$73,738                    60               \$81,393        (\$7,655)     (\$28,371)
56              56                      \$73,738            61              \$83,427        (\$9,690)   ***   56               57                   \$75,581                    61               \$83,427        (\$7,846)     (\$31,633)
57              57                      \$75,581            62              \$85,513        (\$9,932)   ***   57               58                   \$77,471                    62               \$85,513        (\$8,042)     (\$35,104)
58              58                      \$77,471            63              \$87,651       (\$10,180)   ***   58               59                   \$79,407                    63               \$87,651        (\$8,244)     (\$38,796)
59              59                      \$79,407            64              \$89,842       (\$10,435)   ***   59               60                   \$81,393                    64               \$89,842        (\$8,450)     (\$42,721)
60              60                      \$81,393   65 is replaced by 35     \$92,088       (\$10,696)   ***   60               61                   \$83,427           65 is replaced by 35      \$92,088        (\$8,661)     (\$46,892)
61              61                      \$83,427            36              \$45,000        \$38,427    ***   61               62                   \$85,513                    36               \$45,000        \$40,513      (\$51,323)
62              62                      \$85,513            37              \$46,125        \$39,388    ***   62               63                   \$87,651                    37               \$46,125        \$41,526      (\$56,027)
63              63                      \$87,651            38              \$47,278        \$40,373    ***   63               64                   \$89,842                    38               \$47,278        \$42,564      (\$61,019)
64              64                      \$89,842            39              \$48,460        \$41,382    ***   64      65 is replaced by 35          \$92,088                    39               \$48,460        \$43,628      (\$66,316)
65              65                      \$92,088            40              \$49,672        \$42,417    ***   65               36                   \$45,000                    40               \$49,672        (\$4,672)     (\$22,544)
35```
Present value now of fund (\$85,000) (\$72,619) (\$58,900) (\$43,953) (\$27,881) \$10,374 \$9,534 \$8,715 \$7,915 \$7,134 \$6,372 \$5,627 \$4,901 \$4,192 \$3,499 \$2,824 \$2,164 \$1,520 \$891 \$277 (\$322) (\$906) (\$1,477) (\$2,035) (\$2,579) (\$3,110) (\$3,628) (\$4,134) (\$4,628) (\$5,111) (\$5,582) (\$6,041) (\$6,490) (\$6,928) (\$7,355) \$1,181 \$987 \$797 \$612 \$432 \$255 \$83 (\$85) (\$249) (\$409) (\$566) (\$718) (\$867) (\$1,013) (\$1,155) (\$1,293) (\$1,429) (\$1,561) (\$1,690) (\$1,816) (\$1,939) (\$2,058) (\$2,176) (\$2,290) (\$2,401) (\$2,510) (\$2,617) (\$2,721) (\$2,822) (\$2,921) (\$946)