Questions: To help purchase her new car, Amy is taking out a 26,000 amortized loan for 6 years at 5.2% annual interest. Her monthly payment for this loan is 421.14. Fill in all the blanks in the amortization schedule for the loan. Assume that each month is 1/12 of a year. Round your answers to the nearest cent. Payment number Interest payment Principal payment New loan balance --- --- --- --- 1 112.67 308.47 25,691.53 2 25,381.72

To help purchase her new car, Amy is taking out a 26,000 amortized loan for 6 years at 5.2% annual interest. Her monthly payment for this loan is 421.14. Fill in all the blanks in the amortization schedule for the loan. Assume that each month is 1/12 of a year. Round your answers to the nearest cent. Payment number Interest payment Principal payment New loan balance --- --- --- --- 1 112.67 308.47 25,691.53 2 25,381.72
Transcript text: To help purchase her new car, Amy is taking out a $\$ 26,000$ amortized loan for 6 years at $5.2 \%$ annual interest. Her monthly payment for this loan is $\$ 421.14$. Fill in all the blanks in the amortization schedule for the loan. Assume that each month is $\frac{1}{12}$ of a year. Round your answers to the nearest cent. \begin{tabular}{|c|c|c|c|} \hline \begin{tabular}{c} Payment \\ number \end{tabular} & \begin{tabular}{c} Interest \\ payment \end{tabular} & \begin{tabular}{c} Principal \\ payment \end{tabular} & \begin{tabular}{c} New loan \\ balance \end{tabular} \\ \hline 1 & $\$ 112.67$ & $\$ 308.47$ & $\$ 25,691.53$ \\ \hline 2 & $\$ \square$ & $\$ \square$ & $\$ 25,381.72$ \\ \hline \end{tabular}
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Solution

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Solution Steps

Step 1: Calculate Monthly Interest Rate

The monthly interest rate is calculated by dividing the annual interest rate by 12. $$ r_{monthly} = \frac{r}{12} = \frac{0.052}{12} = 0.00433 $$

Step 2: Calculate Interest Payment for Payment Number 2

The interest payment is the remaining loan balance at the beginning of the month times the monthly interest rate. $$ Interest_{payment} = Remaining\_Loan\_Balance \times r_{monthly} = 25691.530 \times 0.00433 = 111.33 $$

Step 3: Calculate Principal Payment for Payment Number 2

The principal payment is the total monthly payment minus the interest payment. $$ Principal_{payment} = M - Interest_{payment} = 421.14 - 111.33 = 309.81 $$

Step 4: Update Loan Balance for Payment Number 2

The new loan balance is the remaining loan balance minus the principal payment. $$ New\_Loan\_Balance = Remaining\_Loan\_Balance - Principal_{payment} = 25691.530 - 309.81 = 25381.72 $$

Final Answer:

For payment number 2, the interest payment is $111.33, the principal payment is $309.81, and the new loan balance is $25381.72.

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