Questions: To help purchase his new minivan, Hong is taking out a 17,000 amortized loan for 6 years at 5.9% annual interest. His monthly payment for this loan is 28094. 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 2 16,604.31 40 41.98 238.96 299.52 41

To help purchase his new minivan, Hong is taking out a 17,000 amortized loan for 6 years at 5.9% annual interest. His monthly payment for this loan is 28094. 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 2 16,604.31 40 41.98 238.96 299.52 41
Transcript text: To help purchase his new minivan, Hong is taking out a $\$ 17,000$ amortized loan for 6 years at $5.9 \%$ annual interest. His monthly payment for this loan is $\$ 28094$. 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 & $\$ \square$ & $\$ \square$ & $\$ \square$ \\ \hline 2 & $\$ \square$ & $\$ \square$ & $\$ 16,604.31$ \\ \hline & & & \\ \hline 40 & $\$ 41.98$ & $\$ 238.96$ & $\$ \$ 299.52$ \\ \hline 41 & $\$ \square$ & $\$ \square$ & $\$ \square$ \\ \hline \end{tabular}
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Solution

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Solution Steps

To fill in the blanks in the amortization schedule, we need to calculate the interest payment, principal payment, and new loan balance for each payment. The interest payment for each month is calculated as the previous month's balance multiplied by the monthly interest rate. The principal payment is the total monthly payment minus the interest payment. The new loan balance is the previous balance minus the principal payment.

Step 1: Calculate Monthly Interest Payment

The monthly interest payment for the first month is calculated using the formula: \[ \text{Interest Payment} = \text{Previous Balance} \times \text{Monthly Interest Rate} \] For the first payment: \[ \text{Interest Payment} = 17000 \times 0.00491667 \approx 83.58 \]

Step 2: Calculate Principal Payment

The principal payment is the total monthly payment minus the interest payment: \[ \text{Principal Payment} = \text{Monthly Payment} - \text{Interest Payment} \] For the first payment: \[ \text{Principal Payment} = 280.94 - 83.58 \approx 197.36 \]

Step 3: Calculate New Loan Balance

The new loan balance is the previous balance minus the principal payment: \[ \text{New Balance} = \text{Previous Balance} - \text{Principal Payment} \] For the first payment: \[ \text{New Balance} = 17000 - 197.36 \approx 16802.64 \]

Step 4: Repeat for Subsequent Payments

Repeat the above steps for the second payment:

  • Interest Payment: \[ 16802.64 \times 0.00491667 \approx 82.61 \]
  • Principal Payment: \[ 280.94 - 82.61 \approx 198.33 \]
  • New Balance: \[ 16802.64 - 198.33 \approx 16604.31 \]

And for the third payment:

  • Interest Payment: \[ 16604.31 \times 0.00491667 \approx 81.64 \]
  • Principal Payment: \[ 280.94 - 81.64 \approx 199.30 \]
  • New Balance: \[ 16604.31 - 199.30 \approx 16405.01 \]

Final Answer

The first three rows of the amortization schedule are:

  1. Interest Payment: \(\boxed{83.58}\), Principal Payment: \(\boxed{197.36}\), New Balance: \(\boxed{16802.64}\)
  2. Interest Payment: \(\boxed{82.61}\), Principal Payment: \(\boxed{198.33}\), New Balance: \(\boxed{16604.31}\)
  3. Interest Payment: \(\boxed{81.64}\), Principal Payment: \(\boxed{199.30}\), New Balance: \(\boxed{16405.01}\)
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