In investments, we all wish we had a crystal ball. Unfortunately, many people need to plan their lives around how much their investments will grow. So, in order to calculate the answer, many financial advisors, insurance salespeople and budget gurus use a simple investment growth calculator such as the one below. The calculator below takes an annual percentage return and applies it to your investments year after year.

Unfortunately, these calculators are useless. Why?

• They don’t factor in inflation. Inflation is a phenomenon that causes money to be worth less with the passage of time. So, pretend you want to retire in 25 years and you want to have all the things a million dollars can buy you in the year 2015. In 25 years, things will cost a lot more because of inflation.

So, let’s say inflation will average 3.4% over the next 25 years. Let’s also say you manage to grow your investments to one million dollars by 2040. Unfortunately, you will find that your million dollars in 2040  can only buy as much as \$420,000 bought in 2015. You would actually have to save \$2,307,000 if you wanted to have all the things a million dollars would have bought you in 2015. Unfortunately, even if you try to subtract 3.4% from your returns to account for inflation, you can’t fix the calculator. That is because….

•The entire premise is flawed. This calculator shows a fundamental misunderstanding of mathematics. In such a calculator, highly variable, compounding factors (investment returns, inflation) are averaged and applied linearly (every single year). This does not work. For instance, pretend you start with \$100,000 and you have an average investment return of 25% over 2 years. This sort of calculator will tell you you have \$156,000 in your investment account. In actuality, you might only have \$100,000. Why? See the two year scenario below for an example:

Year 1: In 2015, you start investing with \$100,000. Your investments decline 50% over the course of the year. You now have \$50,000.

Year 2: At the beginning of 2016, you have \$50,000. Over the course of the year, your investments go up 100%, meaning they double. You are back where you started at \$100,000.

Now, you had two years of returns: -50% and +100%. To find the average, add those numbers together (-50%+100%=50%) and divide that 50% by 2 (50%/2=25%). As you can see, you have an average yearly return of 25% and nothing to show for it. The calculator is clearly flawed, yet many continue to use it. So, how do we do it differently?

• Endress Capital Management uses Monte Carlo simulation, a much more sophisticated approach. Monte Carlo is a mathematical modeling tool that takes historical data and randomizes that data to generate yearly investment returns. For instance, under our Monte Carlo calculator, you might have a -5% return in year one and a 15% return in year two. If you want to know how much money you will have in twenty years, we generate those random numbers for twenty years, ending with one final value.

However, it goes even further. If we generated twenty annual returns and called it a day, you might have gotten very unlucky a couple of years. Maybe you had two years in a row where the stock market declined by 40%. It isn’t likely, but if we just ran the numbers once, very lucky or unlucky scenarios could give you an inaccurate result. So, we run the simulation thousands of times. In this way, we can provide a good estimate of what your return will be over time. Do not let bad math guide your planning; your future is too important.