Compound interest is the interest earned on the principal and on previously earned interest. Let's recall the formula that gives the balance

y

of an account earning compound interest.

y = P (1 + \frac{r}{n})^{n t}

In this formula,

P

is the principal or initial amount,

r

is the annual interest rate written in decimal form,

t

is the time in years, and

n

is the number of times the interest is compounded in one year. Let's pay close attention to the given exercise.

$$ 500$ is deposited in a savings account that earns $9 %$ annual interest compounded monthly.

We can immediately identify

P

as

500 .

Also, the annual interest rate, written as a decimal number, is

0.09 .

Finally, since the interest is compounded monthly and there are

12

months in one year, we have that

n = 12 .

Let's substitute these values into the formula and simplify.

y = P (1 + \frac{r}{n})^{n t}

Substitute values

y = 500 (1 + \frac{0 . 0 9}{1 2})^{12 t}

Calculate quotient

y = 500 (1 + 0.0075)^{12 t}

Add terms

y = 500 (1.0075)^{12 t}

To graph the function we will make a table of values. Since time is always greater than or equal to

0,

we will assign non-negative values for

t .

Let's now plot and connect the obtained points. Since both variables are non-negative, we will only draw in the first quadrant.

Exercise