Nicole takes out a loan for her college tuition from a bank that charges simple interest at an annual rate of \( 16 \% \). Her loan is for \( \$ 5800 \) for 10 months. Assume each month is \( \frac{1}{12} \) of a year. Answer each part below. Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas. (a) Find the interest that will be owed after 10 months. (b) Assuming Nicole doesn't make any payments, find the amount owed after 10 months. \( \$ \) ?

To find the interest owed after 10 months on Nicole's loan, we can use the simple interest formula: \[ \text{Interest} = P \times r \times t \] Where: - \( P = 5800 \) (the principal amount), - \( r = 0.16 \) (annual interest rate), - \( t = \frac{10}{12} \) (time in years, which is 10 months). Calculating the interest: \[ \text{Interest} = 5800 \times 0.16 \times \frac{10}{12} = 5800 \times 0.16 \times 0.8333 = 5800 \times 0.1333 = 773.33 \] So, the interest that will be owed after 10 months is approximately \( \$773.33 \). To find the total amount owed after 10 months, we can just add the interest to the principal: \[ \text{Total Amount Owed} = P + \text{Interest} = 5800 + 773.33 = 6573.33 \] Therefore, the total amount owed after 10 months is approximately \( \$6573.33 \).