To create the amortization schedule for the first three payments of Eric's car loan, let's break down each of the steps involved in calculating the Total Payment, Interest Portion, Principal Portion, and the Balance remaining after each payment.
### Given Data:
- Principal (initial loan amount): \[tex]$13,445.95
- Annual Percentage Rate (APR): 10.5%
- Monthly payment: \$[/tex]226.71
- Number of payments to be calculated: 3
### Key Formulas:
1. Monthly Interest Rate:
[tex]\[
\text{Monthly Interest Rate} = \frac{\text{APR}}{12}
\][/tex]
Since the APR is 10.5%, the monthly interest rate is:
[tex]\[
\frac{10.5\%}{12} = \frac{10.5}{100} \times \frac{1}{12} = 0.00875
\][/tex]
2. Interest Portion (for each month):
[tex]\[
\text{Interest Portion} = \text{Balance} \times \text{Monthly Interest Rate}
\][/tex]
3. Principal Portion (for each month):
[tex]\[
\text{Principal Portion} = \text{Monthly Payment} - \text{Interest Portion}
\][/tex]
4. New Balance:
[tex]\[
\text{New Balance} = \text{Previous Balance} - \text{Principal Portion}
\][/tex]
### Detailed Steps for Each Payment:
#### Before First Payment:
- Previous Balance: \[tex]$13,445.95
#### First Payment:
1. Interest Portion:
\[
13,445.95 \times 0.00875 = 117.65
\]
2. Principal Portion:
\[
226.71 - 117.65 = 109.06
\]
3. New Balance:
\[
13,445.95 - 109.06 = 13,336.89
\]
#### Second Payment:
1. Interest Portion:
\[
13,336.89 \times 0.00875 = 116.70
\]
2. Principal Portion:
\[
226.71 - 116.70 = 110.01
\]
3. New Balance:
\[
13,336.89 - 110.01 = 13,226.88
\]
#### Third Payment:
1. Interest Portion:
\[
13,226.88 \times 0.00875 = 115.74
\]
2. Principal Portion:
\[
226.71 - 115.74 = 110.97
\]
3. New Balance:
\[
13,226.88 - 110.97 = 13,115.91
\]
### Amortization Schedule for the First 3 Payments:
\[
\begin{array}{|c|c|c|c|c|}
\hline \text{Payment Number} & \text{Total Payment} & \text{Interest Portion} & \text{Principal Portion} & \text{Balance} \\
\hline 0 & & & & \$[/tex]13,445.95 \\
\hline 1 & \[tex]$226.71 & \$[/tex]117.65 & \[tex]$109.06 & \$[/tex]13,336.89 \\
\hline 2 & \[tex]$226.71 & \$[/tex]116.70 & \[tex]$110.01 & \$[/tex]13,226.88 \\
\hline 3 & \[tex]$226.71 & \$[/tex]115.74 & \[tex]$110.97 & \$[/tex]13,115.91 \\
\hline
\end{array}
\]
This table shows the breakdown of payments for the first 3 months, detailing the total payment, interest portion, principal portion, and remaining balance after each payment.
