by James Thomas Lee, Jr. 12/25/97 Copyrighted 1995 by James Thomas Lee, Jr. Copyright Number: XXx xxx-xxx
Chapter 10. Getting Into Retirement Analysis {291 words}
a. A Very Useful Equation {229 words}
b. Another Very Useful Equation {265 words}
c. Life In Equilibrium {1,880 words}
d. What The Examples Mean {457 words}
e. An Important Difference Between The Two Examples {427 words}
Chapter 10. Getting Into Retirement Analysis {291 words}
When I left my Government job for SDC, I had another reason for wanting to get into the private sector. In a word, that reason was "retirement!" I had always heard my co-workers talk about the great Civil Service pension plan, but I was not convinced that they were correct. During those days, I wanted to have a more hands-on approach to managing my later-year finances, plus I also wanted to buy stocks! In the late seventies, I had begun to develop an interest in the Stock Market. But I did not know anything about the market, about stock valuation, about what caused the market to go up or down, or about how anyone could ever make any money off of it. I was curious, however, and for me, that meant that I would soon be learning these things and more.
When I got to SDC, I was greeted by a benefit which I had never before encountered - a matching 401-K plan! I could save one dollar in my company 401-K account, and SDC would match it with fifty cents. In 1982, I was still fairly young and was immediately curious to know how much money I could or would have when I retired. I was investing in mutual funds through their plan, yet I also did not know much about mutual funds and how they worked, either. Therefore, I had a lot of questions about all of these various aspects of investing. But I had to be patient and give myself the necessary time to learn.
My first challenge was to figure out how much money I would be able to save by retirement. I have always enjoyed being a mathematician because with math comes power! If a person can understand how to derive equations, then he or she will be virtually unlimited in their ability to do mathematical analysis. I have often been called a Computer Specialist, but my real passion has always been with mathematics. The below equation, which I derived for my company retirement account, has turned out to be something which I have come back to many times. This equation is not simple, but it will tell a person how much he or she can save over time through regular monthly investments. This savings equation, in four separate parts, is as follows:
A = r * [ (1+i)**12n - (1+j)**n ] B = [ (1+i)**12 - 1 ] / i C = [ (1+i)**12 - (1+j) ] D = s * [ (1+i) ** 12n ], where r => amount saved each month i => monthly rate of return j => annual rate on savings increase n => number of years that savings occurs s => initial savings --------------------------------------------------------------------------------------------------------------------- TOTAL SAVINGS = [ ( A * B ) / C ] + D ---------------------------------------------------------------------------------------------------------------------
After deriving the above equation, I started thinking about the same problem but from a different perspective. The above equation dealt with how much a person can save over time by saving a certain amount each month, when adjusted by a cost of living increase factor for each year. Next, I became interested in knowing how much a person would need to save so that he or she could spend a certain amount each month while in retirement. That equation is as follows:
A = (1+i) / [ (1+i)**12n] B = [ (1+i)**12 - 1 ] / i C = [ (1+i)**12n - (1+j)**n ] D = C / [ (1+i)**12 - (1+j) ], where r => amount to be withdrawn each month i => monthly rate of return j => annual rate on withdrawal increase n => number of years withdrawals occur --------------------------------------------------------------------------------------------------------------------- AMOUNT OF MONEY NEEDED = r * A * B * D ---------------------------------------------------------------------------------------------------------------------
As a side note, this "AMOUNT OF MONEY NEEDED" equation can be conveniently modified to show someone how much they can withdraw each month based on the total amount of their savings. That simple modification, which is made by setting the "AMOUNT OF MONEY NEEDED" equal to the "AMOUNT HAD" and solving for "r", yields the following equation:
--------------------------------------------------------------------------------------------------------------------- r = [ AMOUNT HAD ] / [ A * B * D ] ---------------------------------------------------------------------------------------------------------------------
I derived the above equations while working at SDC. A few years later, while consulting to PRC, I came up with another idea for this concept of retirement savings. Most people work their entire life living at one level financially. Then, they retire and take an immediate and sometimes drastic pay cut. To me, that scenario is a signal of unbalanced living. So, I asked myself a simple question. Why not save more while working and then have more to spend in retirement? From that question, my mathematical wheels started to roll, and I soon started to consider what I think of as an ideal financial state.
In my opinion, a person should strive to have the same disposable income each month of their working life and also during their non-working, retirement life. Of course, these monthly amounts have to be adjusted for inflation, but other than that, a person should be able to and even can live a perfectly balanced financial life for most of their adult life. I understand that the first few years of one's work life involves getting established. Once that is done, however, this next system of equations can show someone how to save while working and withdraw while retired in a totally balanced fashion. From a mathematical perspective, the idea is to make "TOTAL SAVINGS" and "AMOUNT OF MONEY NEEDED" equal and then to make the "r" in each of these equations equal after adjusted for inflation. Making these two modifications yields the following, even more complicated system of equations:
E = 1 / [ (1+k)**(12n-1) ]
V = [ (1+k)**12n - (1+m)**n ] / [ (1+k)**12 - (1+m) ]
H = [ (1+k)**12 - 1 ] / k
F = E * V * H
O = [ (1+i)**12(ra-ca) - (1+j)**(ra-ca) ] / [ (1+i)**12 - (1+j) ]
K = [ (1+i)**12 - 1 ] / i
G = K * O
T = s * [ (1+i)**12(ra-ca) ], where
i => monthly rate of return before retirement
j => annual rate of savings increase before retirement
k => monthly rate of return after retirement
m => annual rate of withdrawal increase after retirement
n => number of years in retirement
(ra-ca) => retirement age minus current age (i.e., years until retirement)
s => current savings at the time of the analysis
di=> disposable income (approximately 70% of current monthly salary)
ri=> other annual income during retirement (i.e., Social Security)
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BEGINNING MONTHLY SAVINGS (BMS) = [{di*(1+j)**(ra-ca)-ri}*F - T] / [G+F*(1+j)**(ra-ca)]
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LEFT OVER EACH MONTH (LOEM) = di - BMS
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TOTAL SAVED = BMS * G + T
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A QBASIC version of this program has been provided in Appendix I. For those with Internet accounts, this program can also be executed with a Microsoft Internet Explorer browser from my homepage at "http://members.aol.com/tlee6040". Executing this program will provide the above solution and also list out the savings and withdrawal cycles for each of your future years. Figures 3 and 4 give an example of what one might expect.
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Figure 3. Output from FINSYS.BAS (without Social Security)
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RETIREMENT INPUT DATA
Annual interest rate earned before (xx.x%): 12.0 %
Annual interest rate earned after (xx.x%): 9.0 %
Annual estimated inflation rate before (xx.x%): 3.0 %
Annual estimated inflation rate after (xx.x%): 2.0 %
Your current age (xx): 35
Your planned retirement age (xx): 65
Your current savings ($xxxxxxx.xx): $ 10000.00
Your monthly disposable income ($xxxxx.xx): $ 2250.00
In retirement year dollars, other
retirement funds ($xxxxx.xx): $ 0.00
Planned number years in retirement (xx): 35
OUTPUT RESULTS
Start out saving in the first month: $ 103.18
Amount left over for you: $ 2146.82
Total savings in 30 years will be: $ 812534.75
SAVINGS CYCLE
AGE BEGINNING SAVINGS SAVINGS/MONTH ENDING SAVINGS LEFT OVER
35 $ 10000.00 $ 103.18 $ 12576.79 $ 2146.82
36 $ 12576.79 $ 106.27 $ 15519.64 $ 2211.23
37 $ 15519.64 $ 109.46 $ 18876.16 $ 2277.56
38 $ 18876.16 $ 112.74 $ 22700.01 $ 2345.89
39 $ 22700.01 $ 116.13 $ 27051.71 $ 2416.27
40 $ 27051.71 $ 119.61 $ 31999.50 $ 2488.76
41 $ 31999.50 $ 123.20 $ 37620.31 $ 2563.42
42 $ 37620.31 $ 126.89 $ 44000.85 $ 2640.32
43 $ 44000.85 $ 130.70 $ 51238.88 $ 2719.53
44 $ 51238.88 $ 134.62 $ 59444.60 $ 2801.12
45 $ 59444.60 $ 138.66 $ 68742.23 $ 2885.15
46 $ 68742.23 $ 142.82 $ 79271.80 $ 2971.71
47 $ 79271.80 $ 147.11 $ 91191.12 $ 3060.86
48 $ 91191.12 $ 151.52 $ 104678.07 $ 3152.68
49 $ 104678.07 $ 156.06 $ 119933.16 $ 3247.26
50 $ 119933.16 $ 160.75 $ 137182.34 $ 3344.68
51 $ 137182.34 $ 165.57 $ 156680.33 $ 3445.02
52 $ 156680.33 $ 170.54 $ 178714.14 $ 3548.37
53 $ 178714.14 $ 175.65 $ 203607.27 $ 3654.82
54 $ 203607.27 $ 180.92 $ 231724.30 $ 3764.47
55 $ 231724.30 $ 186.35 $ 263476.13 $ 3877.40
56 $ 263476.13 $ 191.94 $ 299325.78 $ 3993.72
57 $ 299325.78 $ 197.70 $ 339795.09 $ 4113.54
58 $ 339795.09 $ 203.63 $ 385472.13 $ 4236.94
59 $ 385472.13 $ 209.74 $ 437019.63 $ 4364.05
60 $ 437019.63 $ 216.03 $ 495184.44 $ 4494.97
61 $ 495184.44 $ 222.51 $ 560808.19 $ 4629.82
62 $ 560808.19 $ 229.19 $ 634839.38 $ 4768.71
63 $ 634839.38 $ 236.06 $ 718346.75 $ 4911.78
64 $ 718346.75 $ 243.14 $ 812534.75 $ 5059.13
WITHDRAWAL CYCLE
AGE BEGINNING SAVINGS WITHDRAWAL/MONTH ENDING SAVINGS
65 $ 812534.75 $ 5210.90 $ 823091.50
66 $ 823091.50 $ 5315.12 $ 833325.25
67 $ 833325.25 $ 5421.42 $ 843179.38
68 $ 843179.38 $ 5529.85 $ 852591.63
69 $ 852591.63 $ 5640.45 $ 861493.13
70 $ 861493.13 $ 5753.26 $ 869808.06
71 $ 869808.06 $ 5868.32 $ 877453.00
72 $ 877453.00 $ 5985.69 $ 884336.13
73 $ 884336.13 $ 6105.40 $ 890356.38
74 $ 890356.38 $ 6227.51 $ 895402.63
75 $ 895402.63 $ 6352.06 $ 899352.75
76 $ 899352.75 $ 6479.10 $ 902072.56
77 $ 902072.56 $ 6608.68 $ 903414.56
78 $ 903414.56 $ 6740.86 $ 903216.88
79 $ 903216.88 $ 6875.68 $ 901301.81
80 $ 901301.81 $ 7013.19 $ 897474.19
81 $ 897474.19 $ 7153.45 $ 891519.94
82 $ 891519.94 $ 7296.52 $ 883204.31
83 $ 883204.31 $ 7442.45 $ 872269.69
84 $ 872269.69 $ 7591.30 $ 858433.63
85 $ 858433.63 $ 7743.13 $ 841386.44
86 $ 841386.44 $ 7897.99 $ 820788.63
87 $ 820788.63 $ 8055.95 $ 796268.06
88 $ 796268.06 $ 8217.07 $ 767417.00
89 $ 767417.00 $ 8381.41 $ 733788.56
90 $ 733788.56 $ 8549.04 $ 694893.19
91 $ 694893.19 $ 8720.02 $ 650194.56
92 $ 650194.56 $ 8894.42 $ 599105.25
93 $ 599105.25 $ 9072.31 $ 540981.75
94 $ 540981.75 $ 9253.75 $ 475119.38
95 $ 475119.38 $ 9438.83 $ 400746.44
96 $ 400746.44 $ 9627.61 $ 317017.97
97 $ 317017.97 $ 9820.16 $ 223008.78
98 $ 223008.78 $ 10016.56 $ 117705.93
99 $ 117705.93 $ 10216.89 $ 0.49
NOTE that the monthly retirement pension was not included in the above WITHDRAWAL/MONTH amount. That pension should be added into the monthly amount to be withdrawn.
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Figure 4. Output from FINSYS.BAS (with Social Security)
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RETIREMENT INPUT DATA
Annual interest rate earned before (xx.x%): 12.0 %
Annual interest rate earned after (xx.x%): 9.0 %
Annual estimated inflation rate before (xx.x%): 3.0 %
Annual estimated inflation rate after (xx.x%): 2.0 %
Your current age (xx): 35
Your planned retirement age (xx): 65
Your current savings ($xxxxxxx.xx): $ 10000.00
Your monthly disposable income ($xxxxx.xx): $ 2250.00
In retirement year dollars, other
retirement funds ($xxxxx.xx): $ 1000.00
Planned number years in retirement (xx): 35
OUTPUT RESULTS
Start out saving in the first month: $ 70.48
Amount left over for you: $ 2179.52
Total savings in 30 years will be: $ 668979.13
SAVINGS CYCLE
AGE BEGINNING SAVINGS SAVINGS/MONTH ENDING SAVINGS LEFT OVER
35 $ 10000.00 $ 70.48 $ 12162.15 $ 2179.52
36 $ 12162.15 $ 72.60 $ 14625.33 $ 2244.90
37 $ 14625.33 $ 74.78 $ 17428.53 $ 2312.25
38 $ 17428.53 $ 77.02 $ 20615.70 $ 2381.62
39 $ 20615.70 $ 79.33 $ 24236.38 $ 2453.07
40 $ 24236.38 $ 81.71 $ 28346.43 $ 2526.66
41 $ 28346.43 $ 84.16 $ 33008.83 $ 2602.46
42 $ 33008.83 $ 86.69 $ 38294.56 $ 2680.53
43 $ 38294.56 $ 89.29 $ 44283.64 $ 2760.95
44 $ 44283.64 $ 91.96 $ 51066.25 $ 2843.78
45 $ 51066.25 $ 94.72 $ 58744.05 $ 2929.09
46 $ 58744.05 $ 97.56 $ 67431.63 $ 3016.96
47 $ 67431.63 $ 100.49 $ 77258.14 $ 3107.47
48 $ 77258.14 $ 103.51 $ 88369.13 $ 3200.69
49 $ 88369.13 $ 106.61 $ 100928.66 $ 3296.72
50 $ 100928.66 $ 109.81 $ 115121.60 $ 3395.62
51 $ 115121.60 $ 113.10 $ 131156.34 $ 3497.48
52 $ 131156.34 $ 116.50 $ 149267.73 $ 3602.41
53 $ 149267.73 $ 119.99 $ 169720.42 $ 3710.48
54 $ 169720.42 $ 123.59 $ 192812.67 $ 3821.80
55 $ 192812.67 $ 127.30 $ 218880.63 $ 3936.45
56 $ 218880.63 $ 131.12 $ 248303.08 $ 4054.54
57 $ 248303.08 $ 135.05 $ 281506.94 $ 4176.18
58 $ 281506.94 $ 139.10 $ 318973.25 $ 4301.46
59 $ 318973.25 $ 143.28 $ 361244.16 $ 4430.51
60 $ 361244.16 $ 147.58 $ 408930.59 $ 4563.42
61 $ 408930.59 $ 152.00 $ 462721.00 $ 4700.33
62 $ 462721.00 $ 156.56 $ 523391.22 $ 4841.34
63 $ 523391.22 $ 161.26 $ 591815.50 $ 4986.58
64 $ 591815.50 $ 166.10 $ 668979.06 $ 5136.17
WITHDRAWAL CYCLE
AGE BEGINNING SAVINGS WITHDRAWAL/MONTH ENDING SAVINGS
65 $ 668979.06 $ 4290.26 $ 677670.69
66 $ 677670.69 $ 4376.06 $ 686096.38
67 $ 686096.38 $ 4463.59 $ 694209.56
68 $ 694209.56 $ 4552.86 $ 701958.81
69 $ 701958.81 $ 4643.91 $ 709287.56
70 $ 709287.56 $ 4736.79 $ 716133.44
71 $ 716133.44 $ 4831.53 $ 722427.69
72 $ 722427.69 $ 4928.16 $ 728094.69
73 $ 728094.69 $ 5026.72 $ 733051.31
74 $ 733051.31 $ 5127.26 $ 737206.00
75 $ 737206.00 $ 5229.80 $ 740458.19
76 $ 740458.19 $ 5334.40 $ 742697.38
77 $ 742697.38 $ 5441.09 $ 743802.25
78 $ 743802.25 $ 5549.91 $ 743639.44
79 $ 743639.44 $ 5660.91 $ 742062.63
80 $ 742062.63 $ 5774.12 $ 738911.19
81 $ 738911.19 $ 5889.61 $ 734008.88
82 $ 734008.88 $ 6007.40 $ 727162.44
83 $ 727162.44 $ 6127.55 $ 718159.69
84 $ 718159.69 $ 6250.10 $ 706768.06
85 $ 706768.06 $ 6375.10 $ 692732.63
86 $ 692732.63 $ 6502.60 $ 675773.94
87 $ 675773.94 $ 6632.65 $ 655585.50
88 $ 655585.50 $ 6765.31 $ 631831.63
89 $ 631831.63 $ 6900.61 $ 604144.50
90 $ 604144.50 $ 7038.62 $ 572120.94
91 $ 572120.94 $ 7179.40 $ 535319.44
92 $ 535319.44 $ 7322.98 $ 493256.25
93 $ 493256.25 $ 7469.44 $ 445401.66
94 $ 445401.66 $ 7618.83 $ 391175.50
95 $ 391175.50 $ 7771.21 $ 329942.41
96 $ 329942.41 $ 7926.63 $ 261006.66
97 $ 261006.66 $ 8085.17 $ 183606.52
98 $ 183606.52 $ 8246.87 $ 96908.02
99 $ 96908.02 $ 8411.81 $ -1.83
NOTE that the monthly retirement pension was not included in the above WITHDRAWAL/MONTH amount. That pension should be added into the monthly amount to be withdrawn.
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In each of the above two examples, the same input information was provided for both cases. There was only one slight difference between the two, and that difference will be discussed in the next section. The values which were the same are as follows. First, return on investment, which is called annual interest rate before retirement, was set to twelve percent. The annual inflation rate before retirement was set to three percent. After retirement, those two statistics were set to nine and two percent, respectively. Next, for the purpose of the examples, the person performing the analysis was assumed to be thirty-five years old, and their expected retirement age was set to sixty-five. Finally, both examples assumed that the individual had already saved ten thousand dollars and had a monthly disposable income of two thousand, two hundred and fifty dollars. Finally, the number of years for retirement was set to thirty-five.
Several points need to be made about these input data. First, the return on investment after retirement is less than before retirement. The reason is because older people should be investing more conservatively. Second, the after-retirement inflation rate is lower than the before-retirement rate. This lesser amount is not because inflation is expected to be lower. Actually, the inflation rate is used by this program to control annual salary increases. While working, the assumption is that the individual will get a three percent pay raise each year. After retirement, that same person should only allow themselves a two percent allotment increase per year. Third, the number of years of retirement will carry this person out to age one hundred. Most people will not last that long, so why such a lengthy analysis? I can assure you that it is not just to be safe. Actually, it is for the benefit of your heirs.
Notice in the beginning years of the withdrawal cycle that the amount of money steadily grows. In both cases, the amount of funds reaches its maximum at age seventy-seven. Then, it starts to decline. If the person lives to be one hundred, then their cash retirement estate will have dwindled down to zero, give or take a few pennies. However, if that person only lives to be seventy-seven, then their estate will be very large. Even at ninety or ninety-five, the amount of money left behind for their family is quite significant. This financial program will show a person how to live a steady financial life for their entire adult life. Then, assuming a normal life expectancy, the person will have a tidy sum to leave behind for his or her survivors. Proverbs 13:22 says that a good person leaves an inheritance to his or her children's children.
Our nation has begun to enter into a new economic era. In this new era, we no longer want to take care of our elderly because they live too long and also because the Government has probably already squandered most of the Social Security resources. The two examples presented above show the identical financial breakdown, only the second case assumes a one thousand dollar per month Social Security benefit while the first scenario assumes no such benefit. What it will be in the future is anyone's guess. However, the interesting part of all of this is obvious when one examines the two sets of data. In the case where a Social Security benefit is assumed, the individual will be permitted to save less while working and will need to have saved much less by the time of retirement.
Despite what the numbers show, however, Linda and I are not on a Social Security bandwagon. Actually, I do not think that either of us even cares about Social Security. We believe that the Lord will always be able to take care of His people, including us, with or without a Government retirement program. Therefore, our goal is not to take the Social Security Administration or the Government to task over what is happening or has happened in our land. Instead, it is to be more wise with those things and with those people over which the Lord has entrusted us. Most of us can be thankful that the problems of Social Security and longer life spans have been made public. Otherwise, we might all be wasting away our lives and resources and growing old to a future of nothingness and poverty. I am pleased that the Lord revealed this important concern about retirement to me in 1982, that He gave me the ability and interest to derive the equations which have been presented in this chapter, and that He has given Linda and me the time and ability to prepare ourselves for the future. Our God has certainly been good to us!
Chapter 11. The SMART Way To Invest
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