Questions: Keith took out a 5000 loan for 292 days and was charged simple interest. The total interest he paid on the loan was 336. As a percentage, what was the annual interest rate of Keith's loan? Assume that there are 365 days in a year, and do not round any intermediate computations. If necessary, refer to the list of financial formulas. %

Solution Steps

We are given the following information:

• Principal amount (\(P\)) = \$5000
• Total interest paid (\(I\)) = \$336
• Time period (\(t\)) = 292 days
• Number of days in a year = 365

We need to find the annual interest rate (\(r\)) as a percentage.

The formula for simple interest is:

\[ I = P \times r \times t \]

We need to solve for the annual interest rate (\(r\)). Rearrange the formula to solve for \(r\):

\[ r = \frac{I}{P \times t} \]

Since the time period is given in days, we need to convert it to years:

\[ t = \frac{292}{365} \]

Substitute the known values into the rearranged formula:

\[ r = \frac{336}{5000 \times \frac{292}{365}} \]

Calculate the value:

\[ r = \frac{336}{5000 \times 0.8000} = \frac{336}{4000} = 0.084 \]

Convert the decimal to a percentage:

\[ r = 0.084 \times 100\% = 8.4\% \]

Final Answer