Algebra and Trigonometry, 5th Edition

Applications

One of the most frequent applications of exponential functions occurs with compound interest.

Example 4

Compound Interest. The amount of money A to which a principal P will grow after t years at interest rate r (in decimal form), compounded n times per year, is given by the formula

$$A=P{(1+\frac{r}{n})}^{nt}.$$

Suppose that $100,000 is invested at 6.5% interest, compounded semiannually.

1. Find a function for the amount to which the investment grows after t years.

2. Find the amount of money in the account at $t=0,4,8$, and 10 years.

3. Graph the function.

Solution

Technology Connection

We can find the function values in Example 4(b) using the VALUE feature from the CALC menu.

We could also use the TABLE feature.

1. Since $P=\mathrm{\$100},000$, $r=6.5\%=\mathrm{0.065\; ...}$