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 ​$152 comma 000 with a fixed APR of 6​% for 30 years.
Question content area bottom
Part 1
Fill out the table.
End of...
Interest
Payment Toward Principal
New Principal
Month 1
​$

760.00
​$

151.32
​$

151,848.68
​(Round the final answers to the nearest cent as needed. Round all intermediate values to six decimal places as​ needed.)
Part 2
Fill out the table.
End of...
Interest
Payment Toward Principal
New Principal
Month 2
​$

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.)
A home mortgage of $@CNUM{152000} with a fixed APR of 6% for 30 years.A home mortgage of $@CNUM{152000} with a fixed APR of 6% for 30 years.A home mortgage of $@CNUM{152000} with a fixed APR of 6% for 30 years.)))

To fill out the table, let's first break down how to compute the monthly payment, the interest portion, the amount applied to the principal, and the new principal for the mortgage.

### 1. **Monthly Payment Calculation**
The monthly payment $M$ for a mortgage is given by the formula:

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

Where:
- $P = 152,000$ (the loan amount)
- $r = \frac{0.06}{12} = 0.005$ (the monthly interest rate)
- $n = 30 \times 12 = 360$ (the total number of monthly payments)

Let's calculate the monthly payment.

\[
M = 152,000 \times \frac{0.005(1 + 0.005)^{360}}{(1 + 0.005)^{360} - 1}
\]

Using this formula, the monthly payment comes out to approximately:

\[
M \approx 911.32
\]

### 2. **Month-by-Month Breakdown**

For each month, the interest is calculated based on the remaining principal. The portion that goes toward the interest is:

\[
\text{Interest for the month} = \text{Remaining Principal} \times r
\]

The remaining portion of the monthly payment goes toward reducing the principal.

\[
\text{Payment toward principal} = M - \text{Interest for the month}
\]

Finally, the new principal is updated as:

\[
\text{New Principal} = \text{Remaining Principal} - \text{Payment toward principal}
\]

Now, let's compute for the first 3 months.

### **Month 1:**
- **Remaining Principal**: 152,000
- **Interest**: $152,000 \times 0.005 = 760.00$
- **Payment toward principal**: $911.32 - 760.00 = 151.32$
- **New Principal**: $152,000 - 151.32 = 151,848.68$

### **Month 2:**
- **Remaining Principal**: 151,848.68
- **Interest**: $151,848.68 \times 0.005 = 759.2434$ (round to 759.24)
- **Payment toward principal**: $911.32 - 759.24 = 152.08$
- **New Principal**: $151,848.68 - 152.08 = 151,696.60$

### **Month 3:**
- **Remaining Principal**: 151,696.60
- **Interest**: $151,696.60 \times 0.005 = 758.4830$ (round to 758.48)
- **Payment toward principal**: $911.32 - 758.48 = 152.84$
- **New Principal**: $151,696.60 - 152.84 = 151,543.76$

### Completed Table:

| Month | Interest | Payment Toward Principal | New Principal   |
|-------|----------|--------------------------|-----------------|
| 1     | $760.00  | $151.32                  | $151,848.68     |
| 2     | $759.24  | $152.08                  | $151,696.60     |
| 3     | $758.48  | $152.84                  | $151,543.76     |

Would you like more details about any step or further clarification?

### Five related questions:
1. How does the interest payment change over the life of a mortgage?
2. What impact does a higher interest rate have on monthly mortgage payments?
3. How much total interest is paid over the 30 years?
4. How does extra payment toward principal affect the mortgage term?
5. How would the payments change with a 15-year mortgage instead of 30 years?

### Tip:
Making even small additional payments toward the principal can significantly 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 $152,000 with a fixed APR of 6% for 30 years. Fill out the table showing the interest, payment toward principal, and new principal for months 1, 2, and 3.

Learn how to calculate the interest, payment toward principal, and new principal for the first three months of a $152,000 mortgage with a 6% APR over 30 years. This problem demonstrates step-by-step calculations of mortgage amortization using key financial formulas.

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