Due to the effect of compounding interest, large gains on principle can be achieved over a period of many years. For example, suppose one were to invest $100 at an interest rate of 7% for 20 years. Without compound interest, the total at the end of 20 years would be $240.

FV_{simple interest}

However, when the interest earnings from one year are reinvested the next, the following formula is used:

FV_{compound interest}

Substituting 100 for C, 0.07 for r, and 20 for t, we see that

FV_{compound interest}

Clearly, compound interest enables significant gains over a period of many years.

The following diagram shows how $1 will become $10 after 47 years of 5% compound interest: