Questions: A grocery store sells for 181,000 and a 25% down payment is made. A 40-year mortgage at 5% is obtained. Compute an amortization schedule for the first 3 months. Round your answers to two decimal places, if necessary. The value of the mortgage is 135,750 and the monthly payment is 654.32. Part: 0 / 3 Part 1 of 3 Payment number Interest Payment on Principal Balance of Loan 1

A grocery store sells for 181,000 and a 25% down payment is made. A 40-year mortgage at 5% is obtained. Compute an amortization schedule for the first 3 months. Round your answers to two decimal places, if necessary. The value of the mortgage is 135,750 and the monthly payment is 654.32. Part: 0 / 3 Part 1 of 3 Payment number Interest Payment on Principal Balance of Loan 1
Transcript text: A grocery store sells for $\$ 181,000$ and a $25 \%$ down payment is made. A 40 -year mortgage at $5 \%$ is obtained. Compute an amortization schedule for the first 3 months. Round your answers to two decimal places, if necessary. The value of the mortgage is $\$ 135,750$ and the monthly payment is $\$ 654.32$. Part: $0 / 3$ Part 1 of 3 Payment number Interest Payment on Principal Balance of Loan 1 $\$$ $\square$ $\$$ $\square$ $\$$
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Solution

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Solution Steps

To compute the amortization schedule for the first 3 months, we need to follow these steps:

  1. Calculate the interest for the first month by multiplying the loan balance by the monthly interest rate.
  2. Subtract the interest from the monthly payment to get the payment on the principal.
  3. Subtract the payment on the principal from the loan balance to get the new balance.
  4. Repeat the above steps for the next two months.
Step 1: Calculate Monthly Interest for Month 1

The interest for the first month is calculated as: \[ \text{Interest}_1 = \text{Loan Balance} \times \text{Monthly Interest Rate} = 135750 \times 0.004166666666666667 = 565.62 \]

Step 2: Calculate Payment on Principal for Month 1

The payment on the principal for the first month is: \[ \text{Payment on Principal}_1 = \text{Monthly Payment} - \text{Interest}_1 = 654.32 - 565.62 = 88.70 \]

Step 3: Update Loan Balance for Month 1

The new balance of the loan after the first payment is: \[ \text{Loan Balance}_1 = \text{Loan Balance} - \text{Payment on Principal}_1 = 135750 - 88.70 = 135661.30 \]

Step 4: Calculate Monthly Interest for Month 2

The interest for the second month is: \[ \text{Interest}_2 = \text{Loan Balance}_1 \times \text{Monthly Interest Rate} = 135661.30 \times 0.004166666666666667 = 565.26 \]

Step 5: Calculate Payment on Principal for Month 2

The payment on the principal for the second month is: \[ \text{Payment on Principal}_2 = \text{Monthly Payment} - \text{Interest}_2 = 654.32 - 565.26 = 89.06 \]

Step 6: Update Loan Balance for Month 2

The new balance of the loan after the second payment is: \[ \text{Loan Balance}_2 = \text{Loan Balance}_1 - \text{Payment on Principal}_2 = 135661.30 - 89.06 = 135572.24 \]

Step 7: Calculate Monthly Interest for Month 3

The interest for the third month is: \[ \text{Interest}_3 = \text{Loan Balance}_2 \times \text{Monthly Interest Rate} = 135572.24 \times 0.004166666666666667 = 564.88 \]

Step 8: Calculate Payment on Principal for Month 3

The payment on the principal for the third month is: \[ \text{Payment on Principal}_3 = \text{Monthly Payment} - \text{Interest}_3 = 654.32 - 564.88 = 89.44 \]

Step 9: Update Loan Balance for Month 3

The new balance of the loan after the third payment is: \[ \text{Loan Balance}_3 = \text{Loan Balance}_2 - \text{Payment on Principal}_3 = 135572.24 - 89.44 = 135482.80 \]

Final Answer

The amortization schedule for the first three months is as follows:

  • Month 1: Interest = \(565.62\), Payment on Principal = \(88.70\), Balance = \(135661.30\)
  • Month 2: Interest = \(565.26\), Payment on Principal = \(89.06\), Balance = \(135572.24\)
  • Month 3: Interest = \(564.88\), Payment on Principal = \(89.44\), Balance = \(135482.80\)

Thus, the final results are:

  • Month 1: \(\boxed{(565.62, 88.70, 135661.30)}\)
  • Month 2: \(\boxed{(565.26, 89.06, 135572.24)}\)
  • Month 3: \(\boxed{(564.88, 89.44, 135482.80)}\)
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