Sterling70idn
Answered

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Eric financed a new car for [tex]$\$ 12,745.95$[/tex] at an APR of [tex]13.5 \%[/tex] paying [tex]$\[tex]$ 293.28$[/tex][/tex] monthly for 5 years. Create an amortization schedule for the first 3 payments.

Complete the table below.
(Do not round until the final answers. Then round to the nearest cent as needed.)

\begin{tabular}{|c|c|c|c|c|}
\hline
\begin{tabular}{c}
Payment \\
Number
\end{tabular} & \begin{tabular}{c}
Total \\
Payment
\end{tabular} & \begin{tabular}{c}
Interest \\
Portion
\end{tabular} & \begin{tabular}{c}
Principal \\
Portion
\end{tabular} & Balance \\
\hline
0 & & & & \\
\hline
\end{tabular}

Sagot :

GinnyAnsweridn
Sure, let's create the amortization schedule for the first 3 payments based on the provided scenario.

To begin, we have:
- Initial loan amount: [tex]$12,745.95 - Annual Percentage Rate (APR): 13.5% - Monthly payment: $[/tex]293.28
- Term: 5 years (60 months)

First, convert the APR to a monthly interest rate by dividing by 12:
[tex]\[ \text{Monthly interest rate} = \frac{13.5\%}{12} = \frac{0.135}{12} \approx 0.01125 \][/tex]

Let's proceed with calculating the amortization schedule for the first 3 payments.

### Before the first payment (Payment 0)
- Balance: $12,745.95

### Payment 1:
1. Interest Portion: Current balance monthly interest rate
[tex]\[ \text{Interest Portion} = 12,745.95 \times 0.01125 \approx 143.39 \][/tex]

2. Principal Portion: Total monthly payment - interest portion
[tex]\[ \text{Principal Portion} = 293.28 - 143.39 \approx 149.89 \][/tex]

3. New Balance: Current balance - principal portion
[tex]\[ \text{New Balance} = 12,745.95 - 149.89 \approx 12,596.06 \][/tex]

### Payment 2:
1. Interest Portion: Current balance monthly interest rate
[tex]\[ \text{Interest Portion} = 12,596.06 \times 0.01125 \approx 141.71 \][/tex]

2. Principal Portion: Total monthly payment - interest portion
[tex]\[ \text{Principal Portion} = 293.28 - 141.71 \approx 151.57 \][/tex]

3. New Balance: Current balance - principal portion
[tex]\[ \text{New Balance} = 12,596.06 - 151.57 \approx 12,444.49 \][/tex]

### Payment 3:
1. Interest Portion: Current balance * monthly interest rate
[tex]\[ \text{Interest Portion} = 12,444.49 \times 0.01125 \approx 140.00 \][/tex]

2. Principal Portion: Total monthly payment - interest portion
[tex]\[ \text{Principal Portion} = 293.28 - 140.00 \approx 153.28 \][/tex]

3. New Balance: Current balance - principal portion
[tex]\[ \text{New Balance} = 12,444.49 - 153.28 \approx 12,291.21 \][/tex]

### Final amortization schedule for the first 3 payments:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline \text{Payment Number} & \text{Total Payment} & \text{Interest Portion} & \text{Principal Portion} & \text{Balance} \\ \hline 0 & & & & 12,745.95 \\ \hline 1 & 293.28 & 143.39 & 149.89 & 12,596.06 \\ \hline 2 & 293.28 & 141.71 & 151.57 & 12,444.49 \\ \hline 3 & 293.28 & 140.00 & 153.28 & 12,291.21 \\ \hline \end{array} \][/tex]

All values are rounded to the nearest cent as required.
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