The tables show two ways to pay off \( \$ 500 \) in credit card debt. Credit card debt: \( \$ 500 \) Annual compound interest: \( 15 \% \) Payment made per month: \( \$ 15 \) Total paid (44 months): \( \$ 650.85 \) Payment made per month: \( \$ 100 \) Total paid ( 6 months): \( \$ 519.63 \) Which is the best option for someone who wants to improve his or her credit and pay less interest on the debt? \$15 a month because it will let the person keep more spending money \( \$ 100 \) a month because it will free up credit to buy other things \( \$ 15 \) a month because it will save money in the long run \( \$ 100 \) a month because it will reduce the amount of interest paid

To determine the best option for paying off the credit card debt, we need to analyze both payment plans in terms of total interest paid and the time taken to pay off the debt. ### Known Conditions: 1. **Credit Card Debt**: \( \$ 500 \) 2. **Annual Compound Interest Rate**: \( 15\% \) 3. **Option 1**: - Monthly Payment: \( \$ 15 \) - Total Paid (44 months): \( \$ 650.85 \) 4. **Option 2**: - Monthly Payment: \( \$ 100 \) - Total Paid (6 months): \( \$ 519.63 \) ### Step-by-Step Analysis: #### Option 1: Monthly Payment of \( \$ 15 \) - **Total Paid**: \( \$ 650.85 \) - **Interest Paid**: \[ \text{Interest Paid} = \text{Total Paid} - \text{Principal} = 650.85 - 500 = 150.85 \] #### Option 2: Monthly Payment of \( \$ 100 \) - **Total Paid**: \( \$ 519.63 \) - **Interest Paid**: \[ \text{Interest Paid} = \text{Total Paid} - \text{Principal} = 519.63 - 500 = 19.63 \] ### Summary of Findings: - **Option 1**: - Total Interest Paid: \( \$ 150.85 \) - Time to Pay Off: 44 months - **Option 2**: - Total Interest Paid: \( \$ 19.63 \) - Time to Pay Off: 6 months ### Conclusion: - **Interest Comparison**: - Option 1 incurs significantly more interest (\$150.85) compared to Option 2 (\$19.63). - **Time Comparison**: - Option 1 takes much longer (44 months) compared to Option 2 (6 months). ### Best Option: The best option for someone who wants to improve their credit and pay less interest on the debt is: - **\( \$ 100 \) a month because it will reduce the amount of interest paid.** This option not only minimizes the total interest paid but also allows for quicker debt repayment, which is beneficial for credit improvement.