4. Mariette works in construction. She often borrows more than \( \$ 10000 \) to buy supplies. She wants to get a line of credit. a) What type of line of credit should she not get? Justify your answer. b) Mariette got a line of credit. Interest is \( 3.25 \% / y r \), compounded daily. She is going to borrow \( \$ 12329 \) to pay expenses as she renovates a basement. She will pay the balance in 37 d . How much interest will Mariette owe

Sure, let's tackle Mariette's situation step by step. --- ### **a) What type of line of credit should she not get? Justify your answer.** **Mariette should avoid using a **_credit card line of credit_** for her construction-related borrowing needs.** **Justification:** 1. **High Interest Rates:** Credit cards typically come with higher interest rates compared to other forms of credit. For large amounts exceeding \$10,000, the accumulated interest can become substantial, increasing the overall cost of her supplies. 2. **Revolving Debt Risks:** Credit cards are designed for revolving debt, which can encourage ongoing borrowing and make it harder to pay off large balances. This can lead to long-term debt cycles, which are detrimental for business financial health. 3. **Limited Borrowing Capacity:** While some credit cards offer high credit limits, they may not always align with the significant amounts Mariette needs for large projects. This limitation can hinder her ability to secure the necessary funds efficiently. 4. **Inadequate Repayment Terms:** Credit cards usually require minimum monthly payments, which might not be feasible or strategic for managing large, short-term borrowing needs like construction supplies. **Alternative Recommendation:** Instead of a credit card line of credit, Mariette should consider a **business line of credit** or a **term loan** tailored for construction and large-scale projects. These options often provide lower interest rates, higher borrowing limits, and repayment terms that better suit her business operations. --- ### **b) How much interest will Mariette owe?** To calculate the interest owed by Mariette, we'll use the **compound interest formula** since the interest is compounded daily. **Given:** - **Principal (P):** \$12,329 - **Annual Interest Rate (r):** 3.25% or 0.0325 (in decimal) - **Number of Times Interest is Compounded Per Year (n):** 365 (daily compounding) - **Time (t):** 37 days **Steps:** 1. **Convert Time to Years:** \[ t = \frac{37 \text{ days}}{365 \text{ days/year}} \approx 0.10137 \text{ years} \] 2. **Compute the Compound Interest:** The compound interest formula is: \[ A = P \times \left(1 + \frac{r}{n}\right)^{n \times t} \] Plugging in the values: \[ A = 12,329 \times \left(1 + \frac{0.0325}{365}\right)^{365 \times 0.10137} \] \[ A \approx 12,329 \times \left(1 + 0.00008904\right)^{37} \] \[ A \approx 12,329 \times 1.003296 \] \[ A \approx 12,369.64 \] 3. **Calculate the Interest Owed:** \[ \text{Interest} = A - P \] \[ \text{Interest} \approx 12,369.64 - 12,329 = 40.64 \] **Mariette will owe approximately \$40.64 in interest after 37 days.** --- **Summary:** - **a)** Mariette should avoid using a credit card line of credit due to high interest rates and unfavorable repayment terms for large-scale borrowing. - **b)** She will owe roughly \$40.64 in interest after borrowing \$12,329 for 37 days at an annual rate of 3.25% compounded daily.