Questions: Laura took out a 9000 loan for 7 months and was charged simple interest. The total interest she paid on the loan was 336. As a percentage, what was the annual interest rate of Laura's loan? Do not round any intermediate computations. If necessary, refer to the list of financial formulas.

Solution Steps

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

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

where:

• \( I \) is the interest paid ($336)
• \( P \) is the principal amount ($9000)
• \( r \) is the annual interest rate (unknown)
• \( t \) is the time in years (7 months, which is \( \frac{7}{12} \) years)

We need to solve for \( r \):

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

We are given the following values:

• Principal amount, \( P = \$9000 \)
• Total interest paid, \( I = \$336 \)
• Time period in months, \( t = 7 \) months

Since the interest rate is annual, we need to convert the time period from months to years: \[ t_{\text{years}} = \frac{7}{12} \approx 0.5833 \]

The simple interest formula is: \[ I = P \times r \times t \] We need to solve for the annual interest rate \( r \): \[ r = \frac{I}{P \times t} \]

Substitute the given values into the formula: \[ r = \frac{336}{9000 \times 0.5833} \]

Perform the calculation: \[ r \approx \frac{336}{5249.7} \approx 0.0640 \]

Convert the decimal form to a percentage: \[ r \times 100 \approx 6.40\% \]

Final Answer