A mortgage broker is offering a 20-year $179,900 mortgage with a teaser rate. In the first two years of the mortgage, the borrower makes monthly payments on only a 3.6 percent APR interest rate. After the second year, the mortgage interest rate charged increases to 6.6 percent APR. What are the monthly payments in the first two years?

To find the monthly payments for the first two years of the mortgage at the 3.6% APR, we'll use the formula for the monthly payment on a fixed-rate loan:

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

where:
- $ M $ is the monthly payment,
- $ P $ is the principal loan amount (\$179,900),
- $ r $ is the monthly interest rate (annual rate divided by 12 months),
- $ n $ is the total number of payments.

### Step 1: Calculate the Monthly Interest Rate for the First Two Years

The APR for the first two years is 3.6%, so the monthly interest rate is:

\[
r = \frac{3.6\%}{12} = \frac{0.036}{12} = 0.003
\]

### Step 2: Calculate the Number of Payments in the First Two Years

Since the first two years involve 24 monthly payments, $ n $ is 24.

### Step 3: Calculate the Monthly Payment

Now we substitute the values into the formula:

\[
M = 179,900 \frac{0.003(1 + 0.003)^{24}}{(1 + 0.003)^{24} - 1}
\]

Let’s calculate this to find the monthly payment amount.The monthly payments for the first two years of the mortgage at a 3.6% APR interest rate are approximately **$7,780.15**.

Would you like more details or have any questions about this calculation? Here are some related questions you might find useful:

1. How do the monthly payments change after the first two years when the interest rate increases to 6.6%?
2. What would be the total amount paid over the first two years?
3. How much of the first two years' payments go toward interest versus principal?
4. How would the monthly payments change if the initial interest rate were different?
5. What is the total interest paid over the entire 20-year mortgage?

**Tip:** Understanding the breakdown of each monthly payment into principal and interest can help you see how your loan balance decreases over time.

Learn how to calculate the monthly payments for a $179,900 mortgage with a 3.6% APR teaser rate for the first two years. This problem covers key finance concepts, including loan amortization and monthly payment calculations. Suitable for college-level students or those studying finance.

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