Let me walk you through the steps to determine the finance charge, carry-over balance, and minimum payment for each of the next two months.
### Month 1:
1. Calculate the Monthly Interest Rate:
- The Annual Percentage Rate (APR) is [tex]\(18.99\%\)[/tex].
- The monthly interest rate is [tex]\( \frac{18.99\%}{12} \approx 1.5825\% \)[/tex] or 0.015825 as a decimal.
2. Calculate the Finance Charge for Month 1:
- Finance charge (Month 1) = Initial balance [tex]\(\times\)[/tex] Monthly Interest Rate
- Finance charge = [tex]\( \$12,000 \times 0.015825 = \$189.90 \)[/tex]
3. Calculate the New Balance for Month 1:
- New balance (Month 1) = Initial balance + Finance charge
- New balance = [tex]\( \$12,000 + \$189.90 = \$12,189.90 \)[/tex]
4. Calculate the Minimum Payment for Month 1:
- Minimum payment (Month 1) = New balance [tex]\(\times\)[/tex] 5\%
- Minimum payment = [tex]\( \$12,189.90 \times 0.05 = \$609.50 \)[/tex]
### Month 2:
1. Calculate the Carry-Over Balance for Month 2:
- Carry-over balance (Month 2) = New balance (Month 1) - Minimum payment (Month 1)
- Carry-over balance = [tex]\( \$12,189.90 - \$609.50 = \$11,580.40 \)[/tex]
2. Calculate the Finance Charge for Month 2:
- Finance charge (Month 2) = Carry-over balance [tex]\(\times\)[/tex] Monthly Interest Rate
- Finance charge = [tex]\( \$11,580.40 \times 0.015825 = \$183.26 \)[/tex]
3. Calculate the New Balance for Month 2:
- New balance (Month 2) = Carry-over balance + Finance charge
- New balance = [tex]\( \$11,580.40 + \$183.26 = \$11,763.66 \)[/tex]
4. Calculate the Minimum Payment for Month 2:
- Minimum payment (Month 2) = New balance [tex]\(\times\)[/tex] 5\%
- Minimum payment = [tex]\( \$11,763.66 \times 0.05 = \$588.18 \)[/tex]
### Summary Table:
\begin{tabular}{|l|l|l|l|l|}
\hline Month & Carry-over balance & Finance charge & New balance & Minimum payment \\
\hline 1 & 12000 & 189.90 & 12189.90 & 609.50 \\
\hline 2 & 11580.40 & 183.26 & 11763.66 & 588.18 \\
\hline
\end{tabular}
