Lesson 1: How to become a millionaire investing conservatively by the time you retire
The most powerful force in the universe is compound interest. - Albert Einstein
Gilbert Millionaire Spreadsheet
The Excel spreadsheets that are discussed in this article are available for purchase (as an Excel workbook called GilbertMillionaire.xls) by clicking on the Paypal Buy Now button at the bottom of this post for only $9.95.
When I taught a class in personal finance at an urban high school several years ago, a student by the name of Gilbert approached me after class one day and asked me how he could get rich. “How can I become a millionaire?” he asked. I stopped and thought about how to answer such a loaded question. I was impressed with Gilbert’s sincere desire to have a fruitful and productive future. He surely didn’t approach me if he thought that winning a lottery ticket or getting in on some get-rich-quick scheme was the answer. After a few moments of thought, I said that if he came back to me a day or two later I would be better able to answer his question. This gave me the time to design an Excel spreadsheet that would not only answer Gilbert’s question – but to show him both numerically and graphically that by following a disciplined investment savings plan over his working years, he could indeed retire wealthy. Imagine, you too can realistically become a millionaire and retire rich if you know how to harness the power of compounding!
At home that evening I went to work designing a spreadsheet that incorporated simple future value calculations to project the value of a Roth IRA going out 40 years into the future. The spreadsheet may appear to be a bit confusing at first, but with a little guidance it can be quite useful. This spreadsheet, entitled PowerofCompounding_GilbertMillionaire.xls is downloadable on my personal investing blog at www.ProActInvest.net web site.
how to become a millionaire by the time you retire Excel spreadsheet1
Figure 1.1
As you can see from Figure 1.1, the spreadsheet asks you to input certain assumptions such as your starting salary, projected annual pay raises, how much you set aside each year (otherwise known as your savings rate), your expected average annual return from your investments, as well as your tax rate. The tax rate is actually not relevant to this case study, because we are assuming that we can invest the money in a Roth IRA. A Roth IRA is a qualified retirement savings account that anyone with earned income can contribute to up to a certain amount – today that amount is $5,000 per year for most individuals. (The Roth IRA is only accessible by individuals who earn less than $101,000 per year). For further information on Roth IRAs, I suggest consulting the following page on Investopedia’s web site at:
http://www.investopedia.com/articles/retirement/04/091504.asp
Earned income refers to income generated from salary, wages, bonuses commissions or tips – it does not refer to interest income – so retirees who live solely off of interest income from their savings accounts are not allowed to make contributions to qualified retirement plans like a Roth/traditional IRA, 401K, or 403B).
The beauty of the Roth IRA is that you will never be taxed on any of the money that you take out during retirement (any time after age 59 ½ ). This is because the money that you contributed to it during your working years was after-tax (i.e. you did not receive a tax deduction for each dollar contributed as you do with a traditional IRA, 401K, or 403B). As long as you wait at least 5 years after you start making contributions and do not begin taking withdrawals after age 59 ½ you will never be taxed on the money inside a Roth IRA. That’s a wonderful thing, because in a regular taxable brokerage or bank account all your gains (whether interest or capital gains) are taxed, which dramatically cuts into your profits as well as into the growth upon growth effect.
Compound growth is a lot like yeast that grows exponentially. The longer you let the yeast rise, the more dough (quite literally) it will produce. Most of the growth compounding takes place at later stages, not early on. As an example, consider the graph below that charts both compound interest (the red line) as well as simple interest (the blue line). The difference between the two lines is that the blue line does not assume that you reinvest the interest. This would be a situation where someone would live off the interest to pay for living expenses, for example. In this case, the growth portion is basically used up each year and never plowed back into the account. The blue line doesn’t put the interest portion back to work while the red line does. The chart shows that the spread between the two lines increasingly widens over time – so much so that in 40 years the account with compound interest exceeds the arithmetic account by over 4 times.
Compound interest - Exponential vs Arithmetic growth
Let’s return to Gilbert’s spreadsheet for a moment. How much will Gilbert have in his retirement account by age 65 if we make the assumptions (highlighted with the cyan cell background) from Figure 1.1? Will he have enough to retire on? Will Gilbert have $250K, $500K, or $1.0 million? What do you think? If Gilbert starts out his career at age 23 making $35K, receives pay increases averaging 1.5% per year and has the discipline to religiously set aside 10% of his income each month for his Roth IRA, he will have contributed a total of $306,096 by age 65. (See the spreadsheet snapshot below). But what about the growth on these contributions as well as the growth on the growth portions of his investments? It turns out that if we assume an average growth rate of 7.55% on his investments, Gilbert will have amassed a total portfolio value of $1,861,341! If we subtract the $306,096 of contributions to the account, that means that over $1,555,245 of the portfolio end value was due to compound interest (i.e. growth on growth). Amazingly, while it took Gilbert over 40 years of hard work and commitment to this savings and investment program, over half of the growth of the portfolio occurred during the last 9 years (ages 56 – 65)! And, if Gilbert decided to retire 2 years later at age 67 instead of at age 65, the portfolio end value would be $2,185,181 – an increase of $314,029 during the final 2 additional years.
power of compound interest Excel spreadsheet 2
No wonder Einstein was so in awe of the power of compounding! Admittedly, we are making some key assumptions here: for instance, we are assuming that Gilbert remains in good health during his working years and that no major financial catastrophic events occurred in his family. We are also assuming that he is able to stay employed and receives steady pay increases (which at 1.5% per annum are reasonable given that the average rate of inflation in America has been 3.1% per year since 1926). We are also assuming that Gilbert is investing wisely and conservatively. There will be much more on the subject of investing in later lessons (like how to get reasonable returns of over 7% through conservative and moderate growth investment strategies, which by the way, I covered in Gilbert’s class).
George and Martha – or, the importance of starting to save early
Another spreadsheet that I designed for my personal finance class was a hypothetical comparison of the savings behaviors of George and Martha (Washington, one would presume). The spreadsheet emphasizes the importance of starting to save early – of avoiding procrastination. A look at the George and Martha spreadsheet shows us why:
George vs Martha saving early for retirement spreadsheet 1
Martha starts saving $2K per year in her (tax free) Roth IRA. She does this for 8 years, then in year 9 she contributes another $862. For the next 30 years or so, Martha makes no more contributions. From years 1-9, Martha has contributed a total of $16,862 into her retirement account. Meanwhile, George gets off to a slower start. He doesn’t contribute anything until year 9 ($1,138), and then for the next 30 years (until year 40) he is very diligent and contributes $2K per year into his Roth IRA. George has contributed a total of $63,138 into his retirement account. We are also assuming that the average annual return on both retirement accounts is 8%.
The 64 million dollar question is: who has more money in their retirement account in the end – George or Martha?
George vs Martha saving early for retirement spreadsheet 2
One would think that George would end up with more money, having contributed over 3.7 times as much as Martha. Yet the numbers show that George and Martha end up with about the same portfolio end values!
Such is the power of time when it comes to compound growth. While striving for competitive rates of return may be the noble objective of most investors, it is just as important not to lose sight of the importance to start saving early in order to take the fullest advantage of the power of compounding.
Lesson Summary
Let’s wrap up some of the key points from this lesson. In order to take the fullest advantage of the power of compounding, it is important to:
1. Open up a Roth IRA which enables individuals generating earned income to save up to $5K per year. All interest income and capital gains in a Roth IRA are tax free. All withdrawals that you make (after age 59 ½ ) are completely tax free.
2. Start saving at least 10% of your gross income in a qualified retirement account (ideally a Roth IRA). 401Ks are preferable to a Roth only if the company provides a match on your contributions. If the company match is skimpy or non-existent, go with a Roth IRA.
3. Start saving early. As we’ve seen in Gilbert and Martha’s case, in order to take the fullest advantage of the power of compounding, one needs to accumulate as many years as possible. While it’s still better to start late than not at all, many years of growth on growth are foregone – as we saw in George’s case.
4. Starting to save and invest early are more important than shooting for stellar returns. That is, 7% returns with a 10-year head-start are better than 10% returns after the fact. And, in striving for stellar returns, investors often get led astray down paths that are extremely speculative. Better to stick with a solid conservative investment strategy that you can live with.
Relevant Formulas
The formula to project the future value of an investment is FV= P x (1+r)^t
where future value (FV) is equal to the original investment (P) multiplied by (1 + rate of return on the investment) raised to the (t=# of periods) power. Usually, investments compound at annual rates of interest, so t=1. But you can input any time period if you know the average growth rate (r) over a particular time frame. Say for example that your stock portfolio has been averaging a gain of 1.3% per month over the past 4 months. You started out with $10,000 in the account. (We will assume that this is a tax free account like a Roth IRA). To project how much you should have after 12 months you could plug the following numbers into the future value equation:
FV=10,000 x (1 + .013)^12 = 10,000 x 1.16765 = $11,676.52
In order to calculate the periodic return of this investment program, we can use another formula:
% Return = (New – Old ) / Old or verbally, “New minus Old (in parentheses) divided by Old.”
In this case, the year-on-year percent return (always specify the time period when you discuss percentage returns), would be calculated as follows: (11,676.52 – 10,000) / 10,000 = 0.167 = 16.7%
Notice that 16.7% is not equal to 1.3% (the average monthly return) times 12. That would give us 15.6%.
So where did the extra (16.7% - 15.6%=) 1.1% come from? Well, you guessed it –compounding!
Both these formulas can be easily programmed into an Excel spreadsheet, either using the formulas noted above or by plugging in built-in functions in Excel. Just go to Insert/Formulas/Insert Function to access an entire library of built-in functions in Excel. To input the future value formula into a spreadsheet for the above example, type in the following:
=FV(1.3%,12,0,-10000) {1.3% is the average monthly rate of return, 12 is the number of periods, in this case 12 months, 0 is input because we are not making any contributions or withdrawals over the remaining life of the investment program, and -10,000 represents the original investment as a negative number because it is money that we had to plunk down (otherwise known as a cash outflow – outflows are always negative, cash inflows are always positive – don’t worry, you’ll get your money back at the end of the investment program!
I hope that you enjoyed the first lesson in this series on investing.
The Excel spreadsheets that were discussed in this article are available for purchase (as an Excel workbook called GilbertMillionaire.xls) by clicking on the Paypal Buy Now button below for only $9.95.
The GilbertMillionaire wordkbook has tabs to access 6 FREE additional spreadsheets that can help answer questions like:
1. How many years will it take to double my money?
2. Are annuities worth the extra fees?
3. How long will it take me to break even if I suffer a draw-down of 40% or more?
4. Does the order of annual investment returns matter?
5. Does consistency of returns matter?
6. When are (tax free) municipal bonds most suitable to me as an investor?
7. What will the ending value of my investment portfolio be in Z years if I start out with $X, have an annual growth rate of y%, and am subject to a 30% marginal tax rate before retirement and then a 15% tax rate during retirement?
For further information, please consult my web site at
www.proactinvest.net/educational .
Best of luck,
Richard Wiegand
ProActInvest.net
