Answer: To answer the questions, we'll need to perform some calculations based on Francisco's credit card debt and the given APR.
- Time to pay off the debt with minimum monthly payment:
To find out how long it will take Francisco to pay off his debt with the minimum monthly payment, we can use the formula for the number of months it takes to pay off a debt with a fixed monthly payment:
Number of months = -(log(1 - r * (P / A)) / log(1 + r))
where:
r = monthly interest rate (APR divided by 12 and then converted to a decimal)
P = principal amount (credit card debt)
A = fixed monthly payment
Let's calculate:
r = 19.35% / 12 = 0.01935
P = $19,955
A = $200
Number of months = -(log(1 - 0.01935 * (19955 / 200)) / log(1 + 0.01935))
Number of months ≈ 189.61
So, it will take approximately 189.61 months to pay off the debt with a minimum monthly payment of $200.
- Total amount paid to the credit card company with minimum payments:
To calculate the total amount paid to the credit card company, we can use the formula:
Total payment = Number of months * Monthly payment
Total payment = 189.61 months * $200 ≈ $37,922.06
Francisco will wind up paying approximately $37,922.06 to the credit card company by only making the minimum payment.
- Monthly payment to pay off debt in two and a half years:
If Francisco wants to pay off his credit card debt in two and a half years (30 months), we can calculate the required monthly payment using the formula:
Monthly payment = P / N
where:
P = principal amount (credit card debt)
N = number of months (30 months in this case)
Monthly payment = $19,955 / 30 ≈ $665.17
So, Francisco's monthly payment to pay off his credit card debt in two and a half years should be approximately $665.17.