For the following​ loan, make a table showing the amount of each monthly payment that goes toward principal and interest for the first three months of the loan.
A home mortgage of ​$159 comma 000 with a fixed APR of 6​% for 30 years.
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Part 1
Fill out the table.
End of...
Interest
Payment Toward Principal
New Principal
Month 1
​$
  
enter your response here
​$
  
enter your response here
​$
  
enter your response here
​(Round the final answers to the nearest cent as needed. Round all intermediate values to six decimal places as​ needed.)

To calculate the monthly payments and determine how much of each payment goes toward principal and interest, we'll follow these steps:

### Step 1: Calculate the monthly mortgage payment.
The monthly mortgage payment $ M $ for a fixed-rate loan can be calculated using the formula:

\[
M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}
\]

Where:
- $ P $ = Loan principal = $159,000
- $ r $ = Monthly interest rate = $ \frac{6\%}{12} = \frac{0.06}{12} = 0.005 $
- $ n $ = Number of months = 30 years × 12 months/year = 360 months

Let's calculate the monthly mortgage payment:

\[
M = 159,000 \times \frac{0.005(1 + 0.005)^{360}}{(1 + 0.005)^{360} - 1}
\]

### Step 2: Breakdown of Principal and Interest for Each Month
For each month, the interest portion is calculated as:

\[
\text{Interest Payment} = \text{Principal} \times \text{Monthly Interest Rate}
\]

The amount that goes toward the principal is:

\[
\text{Payment Toward Principal} = M - \text{Interest Payment}
\]

Finally, the new principal balance after each payment is:

\[
\text{New Principal} = \text{Previous Principal} - \text{Payment Toward Principal}
\]

Let's calculate the values for the first three months.

### Month 1:
- Initial Principal: $159,000
- Monthly interest rate: 0.005

Interest Payment:
\[
\text{Interest} = 159,000 \times 0.005 = 795.00
\]

Now, we can calculate the total monthly payment:

\[
M = 159,000 \times \frac{0.005(1 + 0.005)^{360}}{(1 + 0.005)^{360} - 1} \approx 954.83
\]

Payment toward Principal:
\[
\text{Principal Payment} = 954.83 - 795.00 = 159.83
\]

New Principal:
\[
\text{New Principal} = 159,000 - 159.83 = 158,840.17
\]

### Month 2:
- New Principal: $158,840.17
- Interest Payment:
\[
\text{Interest} = 158,840.17 \times 0.005 = 794.20
\]
Payment toward Principal:
\[
\text{Principal Payment} = 954.83 - 794.20 = 160.63
\]
New Principal:
\[
\text{New Principal} = 158,840.17 - 160.63 = 158,679.54
\]

### Month 3:
- New Principal: $158,679.54
- Interest Payment:
\[
\text{Interest} = 158,679.54 \times 0.005 = 793.40
\]
Payment toward Principal:
\[
\text{Principal Payment} = 954.83 - 793.40 = 161.43
\]
New Principal:
\[
\text{New Principal} = 158,679.54 - 161.43 = 158,518.11
\]

### Table for the First Three Months:

| Month | Interest Payment | Payment Toward Principal | New Principal Balance |
|-------|------------------|--------------------------|-----------------------|
| 1     | $795.00           | $159.83                  | $158,840.17           |
| 2     | $794.20           | $160.63                  | $158,679.54           |
| 3     | $793.40           | $161.43                  | $158,518.11           |

Would you like more details on how these calculations are done or any other clarification?

### Related Questions:
1. How is the monthly payment formula derived?
2. What is the difference between fixed APR and variable APR loans?
3. How does the principal reduction accelerate over time in such loans?
4. How can you pay off a mortgage early?
5. What are the implications of refinancing a mortgage?

**Tip:** Making extra payments toward the principal can reduce the total interest paid over the life of the loan.

For the following loan, make a table showing the amount of each monthly payment that goes toward principal and interest for the first three months of the loan. A home mortgage of $159,000 with a fixed APR of 6% for 30 years. (Round the final answers to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Understand how to calculate the monthly mortgage payment and create a detailed table of principal and interest payments for the first three months of a $159,000 home mortgage with a 6% fixed APR over 30 years. Learn key concepts like loan amortization and interest calculation, with step-by-step solutions.

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