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 3​% for 30 years.


To analyze this mortgage, we will break down each monthly payment to show how much of it goes toward paying off the principal (the actual loan balance) and how much goes toward interest for the first three months. This calculation is based on a fixed-rate mortgage with an annual percentage rate (APR) of 3% over a 30-year term.

### Step 1: Calculate the monthly payment
The monthly payment for a fixed-rate mortgage is determined by the formula:

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

Where:
- $ M $ is the monthly payment
- $ P $ is the principal loan amount ($152,000)
- $ r $ is the monthly interest rate (annual rate divided by 12)
- $ n $ is the total number of payments (loan term in years times 12 months)

#### Known values:
- $ P = 152,000 $
- APR = 3% or 0.03 annually, which gives a monthly interest rate $ r = \frac{0.03}{12} = 0.0025 $
- Loan term = 30 years, so $ n = 30 \times 12 = 360 $ months

Let's first calculate the monthly payment.

\[
M = 152,000 \times \frac{0.0025(1 + 0.0025)^{360}}{(1 + 0.0025)^{360} - 1}
\]

I'll compute this now.The monthly mortgage payment is approximately **$640.84**.

### Step 2: Break down the first three payments

Now, we'll calculate how much of the monthly payment goes toward the interest and how much goes toward reducing the principal for the first three months.

Each month, the interest is calculated on the remaining principal balance. The amount that goes toward interest in a given month is:

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

The amount that goes toward the principal is the remaining part of the monthly payment:

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

We will repeat this process for the first three months and update the principal balance each month.

Let's calculate the breakdown for each of the first three months.Here is the breakdown of the monthly mortgage payments for the first three months:

| Month | Interest Payment | Principal Payment | Remaining Principal |
|-------|------------------|-------------------|---------------------|
| 1     | $380.00           | $260.84           | $152,000.00          |
| 2     | $379.35           | $261.49           | $151,739.16          |
| 3     | $378.69           | $262.14           | $151,477.67          |

- In the first month, $380.00 goes toward interest and $260.84 goes toward paying down the principal.
- As the principal decreases, the interest portion reduces slightly, and more of your payment goes toward the principal over time.

Would you like more details or have any questions?

---

Here are 5 related questions you might be interested in:
1. How do extra payments impact the overall mortgage cost?
2. How is mortgage amortization calculated?
3. What is the difference between APR and interest rate on a mortgage?
4. How would a shorter loan term (e.g., 15 years) affect monthly payments?
5. How does an adjustable-rate mortgage (ARM) compare to a fixed-rate mortgage?

**Tip**: Making additional principal payments early on can significantly reduce the overall 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 3% for 30 years.

Explore the breakdown of monthly mortgage payments for a $152,000 home loan with a 3% fixed APR over 30 years. Learn how to calculate the amount going toward principal and interest for the first three months using key amortization formulas. Suitable for college-level or advanced high school students.

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