Teresa took out a loan for \( \$ 4800 \) and was charged simple interest at an annual rate of \( 11.5 \% \). The total interest she paid on the loan was \( \$ 138 \). How long was the loan for, in months? Do not round any intermediate computations. If necessary, refer to the list of financial formulas.

To find the duration of the loan in months, we can use the simple interest formula: \[ I = P \cdot r \cdot t \] Where: - \( I \) is the total interest paid, - \( P \) is the principal (loan amount), - \( r \) is the annual interest rate (as a decimal), - \( t \) is the time in years. Given: - \( I = 138 \), - \( P = 4800 \), - \( r = 11.5\% = 0.115 \). Plugging in the values, we have: \[ 138 = 4800 \cdot 0.115 \cdot t \] Now, we can solve for \( t \): \[ t = \frac{138}{4800 \cdot 0.115} \] Calculating the denominator: \[ 4800 \cdot 0.115 = 552 \] Now substituting back in: \[ t = \frac{138}{552} \approx 0.25 \] Since \( t \) is in years, we need to convert it to months: \[ t \text{ (in months)} = 0.25 \text{ years} \times 12 \text{ months/year} = 3 \text{ months} \] Therefore, the loan was for **3 months**.