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 000159,000 

with a fixed APR of 

66​% 

for 30 years.

Question content area bottom

Part 1

Fill out the table.

End of...

Interest

Payment Toward Principal

New Principal

Month 1

​$795.00795.00

​$158.29158.29

​$158,841.71158,841.71

​(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.)

To fill out the table for this home mortgage loan, we first need to calculate the monthly mortgage payment using the fixed APR of 6% over 30 years. 

The mortgage payment formula is given by:

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

Where:
- $ M $ is the monthly payment.
- $ P $ is the loan amount ($159,000).
- $ r $ is the monthly interest rate (annual rate / 12).
- $ n $ is the total number of payments (loan term in months = 30 years × 12 months/year = 360 months).

### Step 1: Calculate the Monthly Payment

The APR is 6%, so the monthly interest rate $ r $ is:

\[
r = \frac{6\%}{12} = \frac{0.06}{12} = 0.005
\]

The number of payments over 30 years is $ n = 360 $.

Using the mortgage payment formula:

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

I’ll calculate the monthly payment first, then proceed with the breakdown for the first three months.The monthly mortgage payment is approximately **$953.29**.

Now, let's calculate the amount of each payment that goes toward interest and principal for the first two months, filling out the table.

### Step 2: Month 1 Breakdown
- Interest = $ \text{Remaining principal} \times r = 159,000 \times 0.005 = 795.00 $
- Principal = Monthly payment - Interest = $ 953.29 - 795.00 = 158.29 $
- New principal = $ 159,000 - 158.29 = 158,841.71 $

### Step 3: Month 2 Breakdown
For the second month:
- Interest = $ \text{New principal} \times r = 158,841.71 \times 0.005 $
- Principal = Monthly payment - Interest
- New principal = Old principal - Principal

Let's calculate these values.For **Month 2**, the breakdown is as follows:
- **Interest:** \$794.21
- **Payment toward principal:** \$159.08
- **New principal:** \$158,682.64

### Final Table for the First Two Months:

| Month | Interest | Payment Toward Principal | New Principal  |
|-------|----------|--------------------------|----------------|
| 1     | $795.00  | $158.29                  | $158,841.71    |
| 2     | $794.21  | $159.08                  | $158,682.64    |

Would you like me to continue for Month 3 or explain any specific part of the calculations? 

Here are five questions for further exploration:
1. How does increasing the interest rate affect the loan breakdown?
2. What happens to the monthly payment if the loan term is reduced?
3. How is the mortgage formula derived from basic interest principles?
4. Why does the interest portion decrease over time while the principal portion increases?
5. How can extra payments reduce the total interest paid?

**Tip:** Making additional payments toward the principal can reduce the loan term and total interest paid.

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.

This problem demonstrates how to calculate the monthly mortgage payment and create an amortization table for a $159,000 home loan with a 6% APR over 30 years. Follow step-by-step breakdowns of how much goes toward interest and principal for the first two months.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation