Invest Like a Professional part 02: The Math

This is a continuation of the post “Invest like a professional: the basics.” So you’re on board with all of the terms on concepts of investing in the stock market. You understand what an index fund is, what bonds are, and you agree investing is a solid endeavor you can deal with. It seems legitimate, but now you’re wondering, how does this really work? Can a regular person really build wealth in the stock market?

How does this really work?

Remember that compound interest formula that makes an enemy of your credit card? Just like it works against you when you spend money, it works for you when you invest money. Being a millennial, being young, is the biggest asset you have when it comes to investing. The biggest mistake people make is thinking “I am only in my 20’s; I don’t need to think about retirement now.” But mathematically speaking, thinking about retirement now and then not thinking about it in your your 40’s is the smarter move. You could literally save for ten years now and be way better off than if you saved more money for 20 years starting when you turn 40.  I want you to understand exactly what your money can do over the next few decades so you can make an informed choice for yourself. You have to weigh all of the options and all of the risks. Don’t just trust some random blogger anymore than you would trust some random financial planner who showed up at your office. Do the work yourself.

Here is our compound interest formula…

And the most important thing to note is that “time” is in the exponent, which means the more time you have, the bigger and bigger the numbers will grow. To make things easier to understand, I am going to assume n=1, or that all of the compounding happens one time per year, say January 1, just so it simplifies the calculations. We want to look at a model that offers an easy comparison. It will be a little more complex in real life, but just one compounding per year, for thirty years, will show you what the payoff could look like for you. So our formula turns into:     

So now our main variables are the principle, or how much we invest at the beginning, the interest rate, and the time. Remember in the Christmas Cash article we talked about IRAs or Individual Retirement Accounts? Anyone can open one of those as long as they have earned income (they’ll get a W2 come January). The maximum one can put in that account is $5500 in a year. So for our example, we are going to assume that you save or invest $5500 all at once. And we want to find out how much this money could be worth 30 years from now. We now have P=5500 and t=30. 

Now, we have a lot of saving and investing options to choose from. We just have to choose our “r” or the interest rate.

Let’s calculate how much money we’d have in a variety of vehicles: a high yield savings account, a CD, and 3 different brokerage accounts. For the sake of this example, it doesn’t matter if it’s an individual or a retirement account; we just want to remember we are analyzing an input of $5500. All of these account types are listed in the first column of the table below. The second column gives the assumed interest rates. Remember that for the stock market, these are not guaranteed in any way. Only for the first two rows would those numbers be guaranteed. The third column shows the math so that you can check it yourself (knowledge is power). The final column shows how much money you would have after letting that $5500 grow for 30 years. There would be no additional investment, just waiting.

As you can see, the higher the interest rate, the higher the ending balance. With an 8% rate of return, your money was multiplied by 10! The 8% rate of return is the common rate used to make predictions about retirement account values, so focus on that number. To get the bigger pay off from the 10% or 12% accounts, you, of course, have to take bigger risks. Historically speaking, the total stock market has grown an average of 12% per year over the last 40 years. We know nothing is guaranteed but if you invest in a total stock market index, you are investing in the American economy as a whole.

Don’t forget about taxes

One thing to remember is that taxes do play into it. While these numbers are just based on the interest rate, the type of account will matter how much, if any, taxes you pay. If you use a regular savings account, that would be money you already paid taxes on, and you will also have to pay taxes on the interest paid to you. If you use a 401(k) or traditional IRA, you will not have to pay any taxes on the money until you’re ready to use it in retirement. If you use a Roth IRA, you pay taxes on the money when it comes through your check, but that potential $100,000 in your account 30 years from now is tax free baby!

Let’s look at it a little differently

I have another visual for you in the graph below. Remember, “time” is our variable that matters most. The more time you give yourself to invest, the more you will have in the end. In this graph you see all the lines begin at $5500 for the account value. The further you move along the x-axis, the wider the gaps get between each of the lines. That means, that the further we move in time, the larger the differences among all of the  accounts become. The green line is the 8% return and the blue line is the 3% return. Notice that if you give it another 10 years, they are even further apart at x=40. The green line reaches an account value of $119,484.87 and the blue line reaches an account value of $17941.21. You will wait the same amount of time, 40 years, but you could have 6.6 times the money just by choosing to invest rather than save.


Remember, this model just looks at a one time investment of $5500. You can invest that much every year until you retire. If you have an employer sponsored fund, you can invest $18,500 every year. Most likely, you’ll save somewhere in the middle. Something is better than nothing. If you save $450 every month, during your working career, you will have over $1 million by the time you retire 35 years from now. This is not counting pensions or social security. All you need to do is make careful diversified investments in index and bond funds. The math is very clear: invest in some way in the American economy to invest in your own future. It is worth it, literally. The more time you give yourself to invest, the more money you’ll have whenever you are ready to retire, whether it’s at 55, 60, or 67.

Share your thoughts!

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