Bought a house for $150,000, with 20% down and at 3 3/4% for 25 years. Provide an amortization schedule for the first three periods?

Let's calculate the amortization schedule for the first three periods.

### Given:
- House price = $150,000
- Down payment = 20% of $150,000 = $30,000
- Loan amount = $150,000 - $30,000 = $120,000
- Interest rate = 3.75% per year (or 0.0375)
- Loan term = 25 years
- Payments per year = 12 (monthly)

#### Monthly Payment Formula:
The formula for calculating monthly mortgage payments (M) is:
\[
M = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1}
\]
Where:
- $P$ is the loan amount ($120,000),
- $r$ is the monthly interest rate (annual rate divided by 12),
- $n$ is the total number of payments (loan term in months).

1. **Monthly Interest Rate**:  
   $ r = \frac{3.75\%}{12} = 0.003125 $

2. **Total Number of Payments**:  
   $ n = 25 \times 12 = 300 $ months

Now, substituting into the formula:
\[
M = 120,000 \times \frac{0.003125(1 + 0.003125)^{300}}{(1 + 0.003125)^{300} - 1}
\]

Let me calculate the monthly payment first.The monthly mortgage payment is approximately **$616.96**.

Now, let's break down the amortization schedule for the first three periods (months). In an amortization schedule, each payment is split between interest and principal. Here's the formula to calculate the amount going to interest and principal:

- Interest for the period = Previous balance $\times$ monthly interest rate
- Principal payment = Monthly payment $-$ Interest
- New balance = Previous balance $-$ Principal payment

Let's calculate these values for the first three months.Here is the amortization schedule for the first three periods (months):

| Month | Payment   | Interest | Principal | Balance    |
|-------|-----------|----------|-----------|------------|
| 1     | $616.96   | $375.00  | $241.96   | $119,758.04|
| 2     | $616.96   | $374.24  | $242.71   | $119,515.33|
| 3     | $616.96   | $373.49  | $243.47   | $119,271.86|

- **Month 1**: $375.00 goes to interest, $241.96 to principal, and the new balance is $119,758.04.
- **Month 2**: $374.24 goes to interest, $242.71 to principal, and the new balance is $119,515.33.
- **Month 3**: $373.49 goes to interest, $243.47 to principal, and the new balance is $119,271.86.

Would you like more details or have any questions?

Here are 5 additional questions for you:
1. How does the principal increase and interest decrease over time in the schedule?
2. How would extra payments affect the loan term and total interest paid?
3. What happens if the interest rate changes after a few years?
4. How does the down payment percentage impact the loan amount and monthly payments?
5. What is the total interest paid over the entire loan term?

**Tip**: Making even small extra payments towards your mortgage principal can significantly reduce the overall interest paid and shorten the loan term!

Explore the amortization schedule for a $120,000 loan with 3.75% annual interest. Learn how to calculate monthly payments and break down principal and interest for the first three months. Understand key amortization concepts and formulas used for loan repayment over 25 years.

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