Numbers and math are not always popular topics, however if you invest in the stock market it is important to know some basic calculations.

Understanding some basic truths about investing thanks to math will help you make decisions based in reality rather than guessing or, worse, assuming the false reality of simple returns.

Two other unpopular topics are inflation and taxes. Both of these real drains on your returns must be factored in to understand how much you actually gained.

How much did your investments really earn last year? You can calculate a rate of return with simple math (don't forget dividends if any), but if you don't adjust it for inflation and taxes, you're not getting the real rate of return.

This is the difference between the nominal interest rate and the real interest rate. You want to know the real rate, since that is the only number that means anything.

Think of it this way: the nominal interest rate tells you the growth rate of your money, while the real interest rate tells you how much your purchasing power is growing.

### Growing Money

For example, if make a $1,000 investment that earns 8% in one year, you end the year with $1,080. In other words, your money has grown by $80 (we'll assume no dividends just to keep the illustration simple).

However if inflation is 3% for the year, your $1,080 is only worth about $1,050. Inflation devalues not only the interest you earned, but the principal too. Your real rate of return is only 5%. See Consumer Price Index.

Investors depending on dividend income or interest from bonds or other fixed-income securities are most directly affected by the costs of inflation. See Understanding Bond Prices and Interest Rates.

If you hold a stock, the gains build up until you sell, so it may be possible to avoid the "inflation tax" if you can time the sale for periods of low inflation.

Stocks can generally weather the effects of inflation better than bonds or other savings instruments. Companies can pass on the higher costs of inflation to customers. Of course, this tends to keep the inflationary cycle going.

### Taxes

The above exercise adjusted your rate of return for inflation; however, it was purely academic unless your investment was in a tax-deferred account or a tax-free investment.

The other deduction you need to take to reach the real rate of return is for taxes. You don't get to keep - in most cases - all the money you make. The government will want its share too.

### Tax Example

Let's return to our example. You invested $1,000 and earned 8% nominal return for $1,080. However, inflation is running 3%, so your real rate of return is only 5% giving you purchasing power of $1,050.

Even though your $1,080 will only buy what $1,050 would one year ago, you still have $1,080 in your account and the government wants a piece. For simplicity sake, let's assume that state and federal taxes totaled 28% in your bracket and that this qualifies as a long-term gain (see link to taxes below)

The government will want $22 of your $80 gain in taxes. Now your real bank account is down to $1,058. See Investing and Taxes

If we reapply the 3% inflation to what you will actually get to keep, we will come up with the real purchasing power your investment returned. This figure is $1,026 (97% of $1,058 = $1,026).

The ugly bottom line is this. Your $1,000 investment has bought you a real return of 2.6% increase in purchasing power over last year after taxes.

That doesn't sound like much, however if you run all investments through the same exercise, you'll find similar results.

### Conclusion

Real returns don't sound as sexy as nominal rates of return, but they are the truth and not an illusion.