Julie borrowed \( \$ 1,900 \) for 8 months from a bank. The bank discounted the loan at \( 5.5 \% \). a. How much interest did Julie pay the bank for the use of its money? b. How much did she receive from the bank? c. What was the actual rate of interest she paid? a. The interest is \( \$ \square \). (Round to the nearest cent as needed.)

To calculate the interest Julie paid the bank, we first need to find the amount of interest using the formula for discounted loans. ### a. Interest Calculation 1. The formula for interest on a discounted loan is: \[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \] 2. Here, the principal (amount borrowed) is \( \$1,900 \), the annual interest rate is \( 5.5\% \) (or \( 0.055 \) when expressed as a decimal), and the time period in years is \( \frac{8}{12} \) (which is \( \frac{2}{3} \) years). 3. Therefore, the interest can be calculated as: \[ \text{Interest} = 1900 \times 0.055 \times \frac{2}{3} = 1900 \times 0.055 \times 0.6667 \approx 55.00 \] So, the interest is \( \$55.00 \). ### b. Amount Received from the Bank To find how much she actually received from the bank, we need to subtract the interest from the principal: \[ \text{Amount Received} = \text{Principal} - \text{Interest} = 1900 - 55 = 1845 \] Julie received \( \$1,845.00 \) from the bank. ### c. Actual Rate of Interest The actual interest paid can be found using: \[ \text{Actual Rate} = \frac{\text{Interest}}{\text{Amount Received}} \times \text{Time in Years} \] In this case, it is: \[ \text{Actual Rate} = \frac{55}{1845} \div \frac{2}{3} \approx 0.0179 (or 1.79\%) \] So, the actual rate of interest Julie paid is approximately \( 1.79\% \). ### Summary: - a. The interest is \( \$55.00 \). - b. She received \( \$1,845.00 \) from the bank. - c. The actual rate of interest she paid was approximately \( 1.79\% \).