Solution

We will solve this problem step by step.

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Part a. Calculate your monthly payments

The formula for calculating the monthly payment for a loan (or credit card debt) is:

$M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1}$

Where:

• $M$: Monthly payment
• $P = 4800$: Initial balance
• $r = \frac{APR}{12} = \frac{19}{100 \cdot 12} = 0.015833$: Monthly interest rate
• $n = 3 \cdot 12 = 36$: Total number of months

Substitute the values:

$M = \frac{4800 \cdot 0.015833 \cdot (1 + 0.015833)^{36}}{(1 + 0.015833)^{36} - 1}$

We will calculate this step-by-step:

1. $1 + 0.015833 = 1.015833$
2. $1.015833^{36} \approx 1.769541$
3. $4800 \cdot 0.015833 = 76$
4. $76 \cdot 1.769541 = 134.485$
5. $1.769541 - 1 = 0.769541$
6. $M = \frac{134.485}{0.769541} \approx 174.78$

So, the monthly payment is approximately $174.78.

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Part b. Total payment

The total payment is the monthly payment multiplied by the total number of months:

$\text{Total Payment} = M \cdot n = 174.78 \cdot 36 = 6292.08$

So, the total payment is approximately $6292.08.

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Part c. Percentage of total payment that is interest

To calculate the interest paid: $\text{Interest} = \text{Total Payment} - \text{Principal} = 6292.08 - 4800 = 1492.08$

The percentage of the total payment that is interest is: $\text{Percentage of Interest} = \frac{\text{Interest}}{\text{Total Payment}} \cdot 100 = \frac{1492.08}{6292.08} \cdot 100 \approx 23.72\%$

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Final Answers

a. Monthly Payment: $174.78
b. Total Payment: $6292.08
c. Percentage of Interest: 23.72%

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Do you want further clarification or step-by-step verification?
Here are some related questions to consider:

1. What if the APR were different, say 15% or 25%?
2. How does the loan term (e.g., 2 years or 5 years) impact the monthly payment and interest?
3. Can you calculate the total interest paid after the first year of payments?
4. What happens if extra payments are made towards the balance?
5. How is the amortization schedule for this loan structured?

Tip: Always ensure to review your credit card terms, as APRs and minimum payments can vary.