Note. The above calculations are approximate when you allow for taxation and inflation. This is due to the timings of tax payments and inflation and the way we are forced to make assumptions about these timings for these calculations. However it does show clearly the effect of taxation and inflation.
For example. Assume you invest $10,000 for 20 years, compounding monthly at 12% per year. Traditional compounding calculations show that you have the staggering sum of $108,925.
However, unless this money is in an IRA or other tax-free vehicle, with zero inflation, you REALLY end up with much less in purchasing power.
For example, with the same numbers above but with an annual tax payment of 30% and 3% inflation, you end up with just $29,252 in real purchasing power terms. In other words. Let's say that you could buy a small car today for $10,000. Save that money for 20 years and you can buy 3 small cars, not 11.
Now try just changing the interest rate to a bank CD rate of 6% per year and the same 30% taxation and 3% inflation. After 20 long years you end up with just over $12,000 in today's money terms.