# Principles of Finance/Section 1/Chapter 2/Time Value of Money/Compounding and FV

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.

FVsimple interest ${\displaystyle =\ C\ +\ t(C*r)}$

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

FVcompound interest ${\displaystyle =\ C\,(1+r)^{t}}$

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

FVcompound interest ${\displaystyle =\ \100\,(1.07)^{20}=\386.97}$

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: