A woman borrowed \( \$ 3400 \) from a bank for 9 months. A friend was cosigner of the woman's personal note. The bank collected \( 5 \frac{1}{2} \% \) simple interest on the date of maturity. a) How much did the woman pay for the use of the money? b) Determine the amount she repaid to the bank on the due date of the note. a) The woman paid \( \$ \square \) for the use of the money.

**Step 1. Calculate the Interest** We first determine the interest amount using the formula for simple interest: \[ I = P \times r \times t \] where \( P = 3400 \) (the principal), \( r = 5.5\% = 0.055 \) (the annual interest rate in decimal form), \( t \) is the time in years. Since the time is 9 months, we convert it to years: \[ t = \frac{9}{12} = 0.75 \] Now substitute the values into the interest formula: \[ I = 3400 \times 0.055 \times 0.75 \] **Step 2. Compute the Interest** Calculate the multiplication step by step: \[ 3400 \times 0.055 = 187 \] Now multiply by \( 0.75 \): \[ 187 \times 0.75 = 140.25 \] Thus, the interest paid for the use of the money is: \[ I = 140.25 \] **Step 3. Determine the Total Amount Repaid** The total amount repaid is the sum of the principal and the interest: \[ \text{Total Repayment} = P + I = 3400 + 140.25 = 3540.25 \] **Answer:** a) The woman paid \( \$140.25 \) for the use of the money. b) The total amount repaid on the due date of the note is \( \$3540.25 \).