Double a Penny Every Day

This tool demonstrates the future values of doubling a penny every day in both a tax-Favored and taxable environment. Use the [Auto-Step] button to automatically step from 1 to 95 days. 30 days is a good place to stop.

Click the graph button below to display a graph showing the results of doubling a penny every day.  The top curve is the tax-favored values.  The bottom curve is the taxed values. Only 10 periods are shown because of the exponential nature of the curve.

Key points illustrated by this tool:

High Returns Enhance Your Wealth

A very high return can enhance your wealth.  In this case, we are using 100% return per day (compounding period).  With this tremendous return, one's wealth grows very quickly, especially in the tax-favored environment.  Notice that the growth is exponential on the right side of the graph.

This increase in wealth growth also happens at lower rates of return.  For example, you will have a much larger retirement accumulation if your assets grow at 10% versus 5%. At a casual glance, one may think the increase in growth would be 5% (10%-5% is 5%) more or twice more (10% is twice 5%). NOT SO!  The difference, as shown by the factor (Tax Favored divided by Taxable) on the right of the dollar amounts is huge! Typically, in real life, we are working with compounding periods of years, as opposed to days, so the time is much longer.  

The point is this: Growth of assets (in a compound growth situation) is not a straight-line function (or curve on a graph). As the rate of return increases, the “curve” turns up more quickly and the curve (or function) growths exponentially.

Trading Can Be Costly

This tool assumes you are taxed each day (compounding period). This is like buying a stock (or asset) each morning and selling it each evening - thus incurring short-term capital gains tax on the proceeds.

However, you can avoid these taxes by holding the asset for a long time. Then you pay one (hopefully) lower tax (long-term capital gains as opposed to short term) when the asset is finally sold. The ideal holding period is forever. However, a more practical holding periods is until death, when the asset is typically marked up in cost basis.  In this scenario, your growth is tax-favored.

No script is provided for this screen.

The equation used to double a penny every day is: New amount = .01 X 2^ (number of days – 1)

The equation used to double a penny every day after tax is: New amount = .01 X (2 – Tax Bracket) ^ (number of days – 1)