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“Unfortunately, no one can be told what the Matrix is. You have to see it for yourself.” – Morpheus, from The Matrix

In some circles, a million dollars is chump change; it takes only minutes for our government to spend that much, and big corporations have many millions pass through their hands in one day “ even during a recession.

But for most individuals, a million is still a big number when it comes to their personal finances. For a long time (probably since the beginning of the 20th century), becoming a millionaire has been a financial milestone for Americans. Even though inflation has dramatically changed the purchasing power of a million dollars, the number is big enough to still have significance. If you have account balances “ in the bank, in your portfolio, in your 401(k) “ that add up to $1,000,000, prevailing wisdom says you’re doing pretty well.

There are a lot of real-life variables involved in accumulating $1 million: career choice, physical health, personal lifestyle, geographic location, the general economic climate, even luck. Ask 10 millionaires for the key ingredients in their success, you’ll probably get 10 different answers.

The real-life variables probably have the greatest impact on whether or not someone will become a millionaire, but some of the mathematical variables “ and the conclusions that can be made from them “ are interesting as well.

Entering the Million-Dollar Matrix
There are three mathematical variables involved in accumulating $1 million:

• Time
• Amount deposited; and
• Rate of return

These three variables are interrelated. The Million-Dollar Matrix shown below is a way to illustrate how changing one item can speed up or slow down one’s progress toward reaching the million-dollar milestone. And a deeper look indicates that different variables have greater importance at different points in the matrix.

Here’s an example to help you use the matrix. Suppose you want to know the monthly deposit that would be needed to accumulate $1 million in 20 years. This information is found in the second shaded column from the left (the one that says œ20 years at the bottom). If you earned a steady annual rate of return of 8% for the entire 20-year period, a deposit of $1,686 would be required each month to realize a $1 million accumulation. If the projected rate of return increased to 12%, the deposit requirement would decrease to $1,001/mo. If the projected rate decreased to 4%, the deposit would have to increase to $2,717/mo.

Remember: The Matrix is not real life “ it’s just math. In real life, the financial variables aren’t static. Rates of return don’t stay the same year after year, so any comparison to actual returns is going to differ (although average rates of return over a specific period will correlate with a steady rate of return over the same time period). The matrix doesn’t make any recommendation about what type of financial vehicles will be used to generate these projected returns, doesn’t factor in any investment risks that might be part of financial instruments that offer the possibility of higher rates of return, and doesn’t consider how taxes might impact any of these decisions.

However¦ the math of the Matrix prompts some interesting thoughts about accumulation. Such as:

The shorter the time period, the greater the emphasis on the size of the deposit. Look at the 5-year column. If you’re starting at zero, and plan to accumulate $1 million in 5 years, it’s all about the size of the deposit. Sure, there’s a difference between depositing $12,123 each month at 12% and $15,835 at 2%, but the 12% earning deposit requirement is a 23% reduction over what’s needed with a 2% annual rate of return. Compare that spread with the 12%-2% difference at 40 years: $84/mo. is 94% less than $1,359/mo.

Look at the comparisons between the 2% and 12% annual returns at the 10- and 15-year periods. While the monthly requirement is almost halved, you still must consider whether the additional investment risk required to earn 12% per year would be worthwhile, especially for extended time periods. If you choose to project a lower rate of annual return (say 6%), the deposit numbers don’t move very much. At any time period less than 20 years, the main ingredient in accumulating $1 million is funding. You must be able to save a lot of money in a relatively short period of time.

With longer time periods, the challenge is consistency, both in deposits and rates of return. As the time period gets longer, the deposit required gets smaller and increased rates of return deliver exponential results. Less money can do more when the time is long and the return is high.

But in longer time frames, it’s easy to see how real-life issues could undo the math. Question: For a responsible, future-oriented 25-year-old, which would be harder: saving $84/mo. for 40 years, or earning 12% a year for 40 years? Answer: Both.

Can you imagine making a monthly savings deposit for 480 months and never missing a payment? Can you imagine an investment that delivers 12% annual returns for 40 years without a hiccup? Math says it’s possible, real life says no. (See the blog post: Buy-and-Hold: Hanging On, or Gone for Good?)

If the higher long-term rates of return are not realistic, this means 40-year savers should set aside more than $84/mo. At a 6% annual rate instead of 12%, our typical 25-year-old needs to save $500/mo. “ for 40 years. That’s a big challenge, for anyone, let alone most 25-year-olds. How many people keep anything “ the same job, the same house “ for 40 years?

If you think you’re getting a late start on accumulation, be cautious about œcatching up by seeking higher returns. According to the Employee Benefits Research Institute’s 2009 survey, released April 16, 2009, almost half of American workers 55 and older reported their savings and investments were less than $50,000 “ and 30% said they had less than $10,000. These are people with a short accumulation horizon, and most of them aren’t close to accumulating $1 million.

Given their circumstances, some older accumulators may feel their only hope is to swing for the investment fences, hoping to hit a financial home run. But remember the math is in the Matrix. A few percentage points in higher returns isn’t going to deliver as much impact as figuring out how to set more aside. Further, if you lose money attempting to achieve a higher return, you have a shorter time to recover the loss.

It’s worth remembering that most Americans at all income levels currently experience their peak earning years between the ages of 45 and 54. This peak earning period has steadily increased over the past 20 years, and there are indications this trend will continue. So, while the monthly deposit to achieve a $1 million dollar accumulation in a short time may seem steep, it’s also possible that your ability to save larger amounts may be ramped up as well.

Where Are You in the Matrix?
Even if the Matrix isn’t real life, the math gives you some things to think about.

As mentioned earlier, saving starts with funding. Once they understand the format, almost everyone who enters the Matrix gravitates toward a time frame that matches their current age and projected retirement. A 40-year-old checks out the columns for 20, 25 and 30 years. A 55-year-old looks at the 10-year column, or if he doesn’t have much savings, scans the 15 and 20-year columns. The rate of return matters, but mostly, you’re checking to see if you can match the required deposits.

This is a natural and productive starting point. œHow much are you saving each month? is a pivotal question, and the Matrix gives you some perspective on whether you ought to be looking to save more, depending on your objectives and circumstances.

Next, there should be a consideration of what you believe is a reasonable rate of return. During the boom years in the financial markets over the past two decades, it was common to believe averaging double-digit annual returns was realistic. Now¦well, most people are less optimistic. It’s not that double-digit returns are out of reach, it’s the awareness that they may also be accompanied by double-digit losses that tends to dampen expectations “ or bring them to more realistic levels.

Assuming a lower rate of return means higher funding levels will be required to reach your objectives. That can be a bummer, because more money allocated to saving for the future means less allocated to spending today. However, overfunding your financial objectives and underprojecting your rate of return is better than the reverse “ underperforming and underfunding would be the worst of both worlds.

Making The Matrix Work For You
In terms of accomplishment, accumulating $1 million by saving is still a big deal. Most millionaires didn’t become millionaires by saving. They did something, owned something, built something, or sold something to acquire their millionaire status. So while it’s mathematically possible for a middle-class American to save his way to $1 million, it’s a project that requires diligence and discipline “ and one that will most likely take a minimum of 15-20 years to accomplish.

If you’re looking for help in the million-dollar Matrix, ask yourself this question: Would you rather work with someone who helps you find a way to

a.) Save $2,568/mo. for 25 years at 2%, or
b.) Save $1,001/mo. for 25 years at 12%

The answer to this question speaks to our perception of that loosely defined term œfinancial planning. Most often, the phrase is used when discussing investment strategies, but there are other possible applications. For example, planning could include strategies for debt structuring, budgeting, tax planning or risk management. If those strategies make it possible to save more money, they are certainly just as valuable, maybe more, than those that focus on trying to squeeze out higher returns.

In general, it is easier, and less risky, to earn 2% than 12%. If a financial professional can show you (through better management of debt, expenses, taxes, etc.) how to meet the demands of the Matrix through higher deposits at lower risk, your chances of succeeding are better than the reverse. The TV stock pickers and newsletter writers get a lot of press when they hit a home run, but you may find that financial efficiency combined with steady, conservative returns gets the job done just as well.

After all, you don’t care where you enter the Matrix. All that matters is if you leave with a million dollars.

WHERE ARE YOU IN THE MATRIX?

IS YOUR FOCUS ON HIGHER RETURN, OR MORE SAVING?

COULD YOU BENEFIT FROM GREATER FINANCIAL EFFICIENCY?