The Power of Compound Interest

The Power of Compound Interest

To illustrate how important “interest on interest” is, we compare the difference in closing balances for an investment earning simple interest and an investment earning compound interest. Consider an amount of \(\text{R}\,\text{10,000}\) invested for \(\text{10}\) years, at an interest rate of \(\text{9}\%\) p.a.

The closing balance for the investment earning simple interest is

\begin{align*} A& = P(1 + in) \\ & = \text{10 000}{(1 + \text{0.09}\times 10)} \\ & =\text{R}\,\text{19,000} \end{align*}

The closing balance for the investment earning compound interest is

\begin{align*} A & = P{(1 + i)}^{n} \\ & = \text{10 000}{(1 + \text{0.09})}^{10} \\ & =\text{R}\,\text{23,673.64} \end{align*}

We plot the growth of the two investments on the same set of axes and note the significant different in their rate of change: simple interest is a straight line graph and compound interest is an exponential graph.

It is easier to see the vast difference in growth if we extend the time period to \(\text{50}\) years:

Keep in mind that this is good news and bad news. When earning interest on money invested, compound interest helps that amount to grow exponentially. But if money is borrowed the accumulated amount of money owed will increase exponentially too.