Questions: You take out a 15 year mortgage for 450000.00 at 4.3% interest. Your monthly payments are 3396.66. Show the amortization schedule for the first 3 months of payments. Use the heading shown below for your schedule. month priorprincipal interest payment endbalance

You take out a 15 year mortgage for 450000.00 at 4.3% interest. Your monthly payments are 3396.66. Show the amortization schedule for the first 3 months of payments. Use the heading shown below for your schedule.
month priorprincipal interest payment endbalance

Transcript text: You take out a 15 year mortgage for $450000.00 at 4.3% interest. Your monthly payments are $3396.66. Show the amortization schedule for the first 3 months of payments. Use the heading shown below for your schedule. month priorprincipal interest payment endbalance

Solution

Solution Steps

To create an amortization schedule for the first three months of a mortgage, we need to calculate the interest for each month, subtract it from the monthly payment to find the principal payment, and then update the remaining balance. The interest for each month is calculated based on the remaining principal balance at the beginning of the month.

Step 1: Calculate Monthly Interest Rate

The annual interest rate is given as $4.3\%$. To find the monthly interest rate, we divide by $12$:

\[ \text{Monthly Interest Rate} = \frac{4.3}{100 \times 12} = 0.0035833333 \]

Step 2: Amortization Schedule for Month 1

For the first month, the prior principal is $450,000.00$. The interest payment is calculated as:

\[ \text{Interest Payment} = 450,000.00 \times 0.0035833333 \approx 1612.50 \]

The principal payment is:

\[ \text{Principal Payment} = 3396.66 - 1612.50 \approx 1784.16 \]

The end balance after the first month is:

\[ \text{End Balance} = 450,000.00 - 1784.16 \approx 448,215.84 \]

Step 3: Amortization Schedule for Month 2

For the second month, the prior principal is $448,215.84$. The interest payment is:

\[ \text{Interest Payment} = 448,215.84 \times 0.0035833333 \approx 1606.11 \]

The principal payment is:

\[ \text{Principal Payment} = 3396.66 - 1606.11 \approx 1790.55 \]

The end balance after the second month is:

\[ \text{End Balance} = 448,215.84 - 1790.55 \approx 446,425.29 \]

Step 4: Amortization Schedule for Month 3

For the third month, the prior principal is $446,425.29$. The interest payment is:

\[ \text{Interest Payment} = 446,425.29 \times 0.0035833333 \approx 1599.69 \]

The principal payment is:

\[ \text{Principal Payment} = 3396.66 - 1599.69 \approx 1796.97 \]

The end balance after the third month is:

\[ \text{End Balance} = 446,425.29 - 1796.97 \approx 444,628.32 \]

Final Answer

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

Month 1: Prior Principal: $450,000.00$, Interest: $1612.50$, Payment: $3396.66$, End Balance: $448,215.84$
Month 2: Prior Principal: $448,215.84$, Interest: $1606.11$, Payment: $3396.66$, End Balance: $446,425.29$
Month 3: Prior Principal: $446,425.29$, Interest: $1599.69$, Payment: $3396.66$, End Balance: $444,628.32$

Thus, the final answer is:

\[ \boxed{\text{Amortization Schedule: Month 1: } 448,215.84, \text{ Month 2: } 446,425.29, \text{ Month 3: } 444,628.32} \]

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