If Timmy takes out a loan for \( \$ 750 \) for 15 months, but only receives \( \$ 725 \) into his bank account, what's the effective interest rate, \( r_{e} \) ? Give your answer as a percentage to the nearest hundredth of a percent. Provide your answer below:

To calculate the effective interest rate \( r_{e} \): 1. First, determine the total interest paid. Timmy takes out a loan of \( \$ 750 \) but only receives \( \$ 725 \), so the interest charged is: \[ \text{Interest} = \$ 750 - \$ 725 = \$ 25 \] 2. Next, find the effective loan amount received. Timmy effectively borrowed \( \$ 725 \) for 15 months. 3. Convert the loan term from months to years: \[ \text{Years} = \frac{15 \, \text{months}}{12 \, \text{months/year}} = 1.25 \, \text{years} \] 4. Now, use the formula for the effective interest rate: \[ r_{e} = \frac{\text{Interest Paid}}{\text{Loan Amount Received}} \times \frac{1}{\text{Loan Term in Years}} \] \[ r_{e} = \frac{25}{725} \times \frac{1}{1.25} \] 5. Calculate \( r_{e} \): \[ r_{e} = \frac{25}{725} \times 0.8 \approx 0.0275862 \] 6. Convert it to a percentage: \[ r_{e} \approx 0.0275862 \times 100 \approx 2.76\% \] Thus, the effective interest rate \( r_{e} \) is approximately **2.76%**.