Frank Has Four Different Credit Cards, The Balances And Interest Information Of Which Are Outlined In The Table Below. He Would Like To Consolidate His Credit Cards To A Single Credit Card With An APR Of $18%$ And Pay Off The Balance In 24
Understanding the Problem
Frank, a financially savvy individual, is facing a common challenge many of us encounter: managing multiple credit cards with varying balances and interest rates. To simplify his financial situation, he wants to consolidate his four credit cards into a single card with an 18% Annual Percentage Rate (APR) and pay off the balance within 24 months. In this article, we will delve into the mathematics behind credit card consolidation and explore the best approach for Frank to achieve his goal.
The Current Credit Card Situation
| Credit Card | Balance | APR | Minimum Payment |
|---|---|---|---|
| Card 1 | $2,000 | 20% | $50 |
| Card 2 | $1,500 | 22% | $37.50 |
| Card 3 | $3,000 | 19% | $75 |
| Card 4 | $1,000 | 21% | $25 |
Calculating the Total Debt
To begin, let's calculate the total debt Frank needs to pay off. We can do this by adding up the balances of all four credit cards.
Total debt = $2,000 + $1,500 + $3,000 + $1,000 = $7,500
The Benefits of Consolidation
Consolidating credit cards can provide several benefits, including:
- Simplified payments: By consolidating his credit cards, Frank will only need to make one monthly payment, reducing the complexity of managing multiple credit cards.
- Lower interest rates: The 18% APR on the new credit card is lower than the APRs on three of Frank's current credit cards, which can save him money on interest charges.
- Reduced debt: Consolidating his credit cards can also help Frank pay off his debt faster, as he will only need to make one payment per month.
The Mathematics of Consolidation
To consolidate his credit cards, Frank will need to calculate the total amount he needs to pay each month to pay off the debt within 24 months. We can use the formula for calculating monthly payments on a loan:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]
Where: M = monthly payment P = principal loan amount (total debt) i = monthly interest rate (APR / 12) n = number of payments (24 months)
Calculating the Monthly Payment
First, let's calculate the monthly interest rate:
i = 18% / 12 = 1.5% per month
Next, we can plug in the values into the formula:
M = $7,500 [ 1.5(1 + 1.5)^24 ] / [ (1 + 1.5)^24 – 1]
M ≈ $335.19
The Total Interest Paid
To calculate the total interest paid, we can use the formula:
Total interest = P – P(1 + i)^n
Where: P = principal loan amount (total debt) i = monthly interest rate (APR / 12) n = number of payments (24 months)
Plugging in the values, we get:
Total interest = $7,500 – $7,500(1 + 1.5)^24 Total interest ≈ $1,434.19
Conclusion
In conclusion, Frank's credit card consolidation dilemma can be solved using the mathematics of loans. By consolidating his credit cards into a single card with an 18% APR and paying off the balance within 24 months, Frank can simplify his financial situation, reduce his interest rates, and pay off his debt faster. The total interest paid will be approximately $1,434.19, and the monthly payment will be $335.19.
Recommendations
Based on the calculations, we recommend that Frank:
- Consolidate his credit cards: Frank should consolidate his credit cards into a single card with an 18% APR to simplify his financial situation and reduce his interest rates.
- Make timely payments: Frank should make timely payments of $335.19 per month to pay off the debt within 24 months.
- Monitor his credit report: Frank should monitor his credit report to ensure that the consolidation is reported correctly and that his credit score is not affected.
Understanding the Problem
Frank, a financially savvy individual, is facing a common challenge many of us encounter: managing multiple credit cards with varying balances and interest rates. To simplify his financial situation, he wants to consolidate his four credit cards into a single card with an 18% Annual Percentage Rate (APR) and pay off the balance within 24 months. In this article, we will delve into the mathematics behind credit card consolidation and explore the best approach for Frank to achieve his goal.
Q&A: Credit Card Consolidation
Q: What is credit card consolidation?
A: Credit card consolidation is the process of combining multiple credit card debts into a single loan with a lower interest rate and a single monthly payment.
Q: Why should I consolidate my credit cards?
A: Consolidating your credit cards can provide several benefits, including simplified payments, lower interest rates, and reduced debt.
Q: How do I calculate the total debt?
A: To calculate the total debt, add up the balances of all your credit cards.
Q: What is the formula for calculating monthly payments on a loan?
A: The formula for calculating monthly payments on a loan is:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]
Where: M = monthly payment P = principal loan amount (total debt) i = monthly interest rate (APR / 12) n = number of payments (24 months)
Q: How do I calculate the total interest paid?
A: To calculate the total interest paid, use the formula:
Total interest = P – P(1 + i)^n
Where: P = principal loan amount (total debt) i = monthly interest rate (APR / 12) n = number of payments (24 months)
Q: What is the total interest paid in Frank's case?
A: The total interest paid in Frank's case is approximately $1,434.19.
Q: What is the monthly payment in Frank's case?
A: The monthly payment in Frank's case is approximately $335.19.
Q: How can I ensure that my credit card consolidation is successful?
A: To ensure that your credit card consolidation is successful, make timely payments, monitor your credit report, and avoid taking on new debt.
Q: What are the benefits of credit card consolidation?
A: The benefits of credit card consolidation include simplified payments, lower interest rates, and reduced debt.
Q: Can I consolidate my credit cards with a credit card company?
A: Yes, you can consolidate your credit cards with a credit card company. However, be sure to research and compare rates and terms before making a decision.
Q: What are the risks of credit card consolidation?
A: The risks of credit card consolidation include taking on new debt, higher interest rates, and longer repayment periods.
Conclusion
In conclusion, credit card consolidation can be a powerful tool for simplifying your financial situation and reducing your debt. By understanding the mathematics behind credit card consolidation and following the recommendations outlined in this article, you can achieve your goal of consolidating your credit cards and paying off your debt within a reasonable timeframe.
Recommendations
Based on the calculations, we recommend that Frank:
- Consolidate his credit cards: Frank should consolidate his credit cards into a single card with an 18% APR to simplify his financial situation and reduce his interest rates.
- Make timely payments: Frank should make timely payments of $335.19 per month to pay off the debt within 24 months.
- Monitor his credit report: Frank should monitor his credit report to ensure that the consolidation is reported correctly and that his credit score is not affected.
By following these recommendations, Frank can achieve his goal of consolidating his credit cards and paying off his debt within 24 months.