3. Cynthia is a DJ In Kamloops, She has a MasterCard. The credlt llmit is \( \$ 4000 \). Interest is \( 19.8 \% / y r \), compounded dally. She used all her credil on the card to buy some new DJ equipment. Cynthla took 49 d after the grace period to pay the balance. a) Do you think Cynthla was wise to buy the equipment with her credit card? Explain. b) How much interest did Cynthia pay? c) What other way might Cynthia have paid for her equipment? d) What method of financing would be unwise? Justify your answer.

Let's address each part of Cynthia's situation systematically: ### a) Was it wise for Cynthia to buy the equipment with her credit card? Explain. **Assessment:** Using a credit card to finance significant purchases like DJ equipment can be a double-edged sword. On one hand, it provides immediate access to the funds needed without the need for collateral or a lengthy loan approval process. On the other hand, credit cards typically carry high-interest rates, especially if the balance isn't paid off promptly. **In Cynthia's Case:** - **Pros:** - **Convenience:** She could purchase the equipment immediately, enabling her to continue or expand her DJ services without delay. - **Build Credit History:** Timely payments can positively impact her credit score. - **Cons:** - **High-Interest Rates:** With an annual interest rate of 19.8%, carrying a balance incurs significant interest charges. - **Potential Debt Accumulation:** If unable to pay off the balance quickly, interest can compound, leading to a larger debt over time. **Conclusion:** While using a credit card provided Cynthia with immediate funds, the high-interest rate means it was only a wise choice if she was confident in paying off the balance promptly to avoid substantial interest charges. ### b) How much interest did Cynthia pay? **Given:** - **Principal (P):** \$4,000 - **Annual Interest Rate (r):** 19.8% - **Time (t):** 49 days - **Compounding Frequency:** Daily **Calculations:** 1. **Determine the Daily Interest Rate:** \[ \text{Daily Rate} = \frac{19.8\%}{365} \approx 0.0542\% \text{ per day} \] 2. **Calculate the Interest Using Daily Compounding:** \[ A = P \times \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( n = 1 \) (since it's compounded daily) - \( t = \frac{49}{365} \) years \[ A = 4000 \times \left(1 + \frac{0.198}{365}\right)^{49} \approx 4000 \times 1.027 \approx \$4,108 \] 3. **Interest Paid:** \[ \text{Interest} = A - P = 4108 - 4000 = \$108 \] **Therefore, Cynthia paid approximately \$108 in interest.** ### c) What other ways might Cynthia have paid for her equipment? **Alternative Financing Options:** 1. **Personal Loan:** - **Pros:** Typically lower interest rates compared to credit cards. - **Cons:** Requires credit approval and may involve origination fees. 2. **Savings:** - **Pros:** No interest or debt incurred. - **Cons:** Depletes personal savings, which might be needed for emergencies. 3. **0% APR Credit Card Offers:** - **Pros:** Interest-free period allows for interest-free financing if paid within the promotional period. - **Cons:** If the balance isn't paid in time, high-interest rates may apply retroactively. 4. **Equipment Financing or Leasing:** - **Pros:** Tailored specifically for equipment purchases, sometimes with lower rates. - **Cons:** May require collateral or have strict terms. 5. **Business Loan or Line of Credit:** - **Pros:** Potentially lower interest rates and longer repayment terms. - **Cons:** Requires business creditworthiness and may involve more paperwork. **Recommendation:** A personal loan or equipment financing would likely offer lower interest rates compared to a credit card, reducing the overall cost of financing the equipment. ### d) What method of financing would be unwise? Justify your answer. **Unwise Financing Method: Payday Loans** **Reasons:** 1. **Extremely High-Interest Rates:** - Payday loans often come with exorbitant interest rates, sometimes exceeding 300% APR. 2. **Short Repayment Terms:** - Typically require repayment within two weeks, which can lead to financial strain. 3. **Debt Cycle Risk:** - Borrowers may find themselves unable to repay on time, leading to rollovers, additional fees, and escalating debt. 4. **Minimal Regulation:** - In many regions, payday lenders are minimally regulated, offering little protection to borrowers. **Conclusion:** Using payday loans would be highly unwise for Cynthia due to the prohibitive costs and the high risk of falling into a debt cycle, which could severely impact her financial stability and creditworthiness.