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Author: GCollier One star, 50 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: of 25234  
Subject: Who Wants To Retire As A Millionaire? Date: 8/19/2000 5:06 PM
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I was fascinated that someone age 19 (see Post # 8901) has already begun the process of LBYM and saving for retirement. Unfortunately, most of us did not take this message to heart at an early age. However, it is critical that we get our children to thinking in these terms unless you believe that Social Security will do an adequate job of taking care of them. The first question everyone asks (usually after their 40th birthday) is "How much will I need at retirement?" I will not address this question but suggest that younger folks response should be "As much as I can accumulate". The second question which everyone needs to understand is - "If I invest $x dollars each year, what is the expected value of my nest-egg at retirement?" I will try to address this latter question with an illustration of why it is so important to begin investing when we are younger.

Following is an exercise which I used to challenge (hopefully educate) my two children about the benefits of investing for compounded growth. COMPOUND GROWTH (i.e., compound interest) of equity valuations in the U.S. stock market is the only reason that most of us have any hope of financial security during our retirement years. Unless one plans to rely on Social Security for retirement, it is critcial that he/she learns strategy of investing for compound growth early in their career. All of us are familiar with the term "compound interest" which we pay on a loan - for example, interest you pay when buying a house. For financial security during retirement, each of us needs to reverse this process and gain wealth throughout our working career by investing for compounded growth. This simple principle is the reverse of compounded interest but its effect on our financial well-being during retirement is astounding.

First, let us make a few simplifying assumptions:
* Today is your birthday (Jan 1) and you are 20 years of age
* You will make $1000 investment each Jan 1
* You plan to achieve 11% return EACH year until you retire
(11% is historical average of S&P 500 Index)
* You plan to retire on your 65th birthday after which you will begin
withdrawing money from your savings

Second, let us explore two investment scenarios:
1) You invest your first $1000 on your 20th birthday (today) and continue
each Jan 1 through your 29th birthday after which you make no more investments.
* Number of Investing Periods = 10 (i.e., Total = $10,000)
* Number of Non-Investing Periods = 35
2) You make your first $1000 investment on your 30th birthday and then
$1000 each Jan 1 for 34 more years (i.e., thru age 64).
* Number of Non-Investing Periods = 10
* Number of Investing Periods = 35 (i.e., Total = $35,000)

QUESTION: Under which investment scenario would you have the largest nest-egg at retirement. (Hint: You will likely be astonished by the answer.)

For the mathematically challenged among us, the question is "How can I possibly calculate the 'expected value' of my portfolio at age 65?" If we dust off our math book, we find two equations we need: annuity and compound interest. The annuity equation is used to calculate expected value of our portfolio following those years when we make our yearly investments. The compound interest equation is used to calculate expected value of our portfolio following those years when we did not make yearly investments. Thus, we would use the two equations as follows:

Beginning Age = 20 years - Apply the annuity equation to calculate value of your portfolio on your 30th birthday. Next, apply the compound interest
equation to calculate value of your portfolio on your 65th birthday by using expected value of your portfolio at age 30 as the principal amount.

Beginning Age = 30 years - Use the annuity equation to calculate expected value of your investment on your 65th birthday.

The two equations are:
* Annuity: Expected Value = $1000 x (((1 + .11)exp n) - 1) / .11
where $1000 = yearly investment
n = number of years
.11 = expected rate of return

* Compound Interest: Expected Value = P x (1 + .11)exp n
where P = Beginning Principal
.11 = expected rate of return
n = number of years

Our Example Scenarios:
Age = 20 Years - Ten yearly investments with compounded growth followed by 35 years of compounded growth

* Expected Value at Age 30: E.V. = 2.8395/.11 x $1000 = $25,814
* Expected Value at Age 65: E.V. = $25,814 x 38.5785 = $995,865

Age = 30 Years - 35 yearly investments with compounded growth

* Expected Value at Age 65: E.V. = $1000 x 38.5785/.11 = $350,714

Based on our assumptions (and assuming I did not make an arithmetic error), an individual investing for only ten years should expect nest-egg at age 65 to equal $995,865 while that individual who started investing at age 30 should expect a nest-egg worth only $350,714. You can adjust the number of years to retirement as well as the expected compound growth rate but the message is still the same. If you want to be financially secure during retirement, start investing at the earliest possible age.
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