Finding the principal, rate, or time of a simple... Ann borrowed $$ \$ 200 $$ from a bank for 4 years and was charged simple interest. The total interest that she pa was $$ \$ 56 $$. As a percentage, what was the annual interest rate of her loan? If necessary, refer to the list of financial formulas. $$ \square \% $$

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To find the annual interest rate of Ann's loan, we can use the formula for simple interest:

$$
I = P \times r \times t
$$

Where:
- $$ I $$ is the interest earned (or paid),
- $$ P $$ is the principal amount (the initial amount of money),
- $$ r $$ is the annual interest rate (as a decimal),
- $$ t $$ is the time in years.

From the problem, we know:
- $$ I = 56 $$ (the total interest paid),
- $$ P = 200 $$ (the principal amount borrowed),
- $$ t = 4 $$ (the time in years).

We need to find $$ r $$. Rearranging the formula to solve for $$ r $$:

$$
r = \frac{I}{P \times t}
$$

Now, we can substitute the known values into the equation:

$$
r = \frac{56}{200 \times 4}
$$

Calculating the denominator:

$$
200 \times 4 = 800
$$

Now substituting back into the equation for $$ r $$:

$$
r = \frac{56}{800}
$$

Now we can calculate $$ r $$:

$$
r = 0.07
$$

To express $$ r $$ as a percentage, we multiply by 100:

$$
r = 0.07 \times 100 = 7\%
$$

Thus, the annual interest rate of Ann's loan is $$ 7\% $$.
The annual interest rate of Ann's loan is 7%.

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