Blog #59 Dollar Average Compounding

I hope you find the formula given in the previous blog interesting. You can use the formula to estimate your median future wealth after investing $X for a specified number of years. In the example given, X is $100,000 and the geometric mean return is 4.88% per year. After 30 years, $100,000 grows to about about $420,000.  Remember that this is your median wealth. Due to uncertainty, your actual wealth can be higher or lower than the median. That said, the median wealth is still a useful number because it corresponds to the midpoint of the wealth range.

While a sum of $420,000 is pretty inspiring, most people don’t have $100,000 to plonk into the stock market at one go.  Instead, most of us invest bit by bit, say $10,000 every year or $834 each month. The bad news is that the previous formula doesn’t work in this case. The good news: there is another formula which does!

The new formula applies to an investor who invests a constant $Y every year or grows this amount by a constant rate each year. Throughout his investment journey, the stock market is assumed to earn a specified average rate of return with a specified level of risk. The question the investor wants to know is: “after N years, how much wealth can I expect to have?”.

The new formula isn’t as simple as the previous formula, so I won’t show it here. Instead, to make things user-friendly, I’ve coded it in Excel as a wealth calculator which you can download here.

The input section of the calculator looks like this:


All you have to do is key in the  inputs in the gray cells. They are: AM is the arithmetic mean rate of return (in percent per year), Volatility is the standard deviation of annual returns, Contributions refer how much you wish to invest each year starting now and Annual Increase is the rate at which you want to grow your annual investments. The wealth calculator will automatically project your future median wealth for various periods in the future from 10 to 35 years as shown. That’s it!

In the example shown here, you think that the long-term arithmetic mean return of the stock market is 8% and the volatility is 20%. With these inputs, the geometric mean is automatically calculated for you and then modified to project the future median wealth (details in the spreadsheet). The output (black cells) shows that if you invest $10,000 (starting now) for say 10 years, you can expect a median wealth of $156,438. If you double your investment horizon, the median wealth is more than double to $432,659 and so on.


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