A college student takes out a \( \$ 7,500 \) loan from a bank. What will the balance of the loan be after one year (assuming the student has not made any payments yet): a. If the bank charges \( 3.8 \% \) interest each year? b. If the bank charges \( 5.3 \% \) interest each year?

1. **Identify the formula for the balance after one year.** The balance \( B \) after one year with interest rate \( r \) is calculated as: \[ B = P \times (1 + r) \] where \( P \) is the principal (initial loan) and \( r \) is the interest rate (expressed as a decimal). 2. **Calculate the balance for \( 3.8\% \) interest.** - Convert the interest rate to a decimal: \[ r = 0.038 \] - Substitute into the formula with \( P = 7500 \): \[ B = 7500 \times (1 + 0.038) = 7500 \times 1.038 \] - Compute the multiplication: \[ B = 7785 \] - **Answer for (a):** The balance after one year is \( \$7785 \). 3. **Calculate the balance for \( 5.3\% \) interest.** - Convert the interest rate to a decimal: \[ r = 0.053 \] - Substitute into the formula with \( P = 7500 \): \[ B = 7500 \times (1 + 0.053) = 7500 \times 1.053 \] - Compute the multiplication: \[ B = 7897.5 \] - **Answer for (b):** The balance after one year is \( \$7897.5 \).