A mortgage broker is offering a $225,000 30-year mortgage with a teaser rate. In the first two years of the mortgage, the borrower makes monthly payments on only a 2.5 percent APR interest rate. After the second year, the mortgage interest rate charged increases to 8.5 percent APR. What are the mortgage payments in the first two years? What are the mortgage payments after the second year?

To calculate the mortgage payments in the first two years, we need to find the monthly payment based on the 2.5 percent APR interest rate.

Step 1: Convert the APR interest rate to a monthly rate. Divide the APR by 12 months.
2.5% / 12 = 0.0208 or 0.02 (rounded to two decimal places)

Step 2: Calculate the monthly interest rate by multiplying the loan amount by the monthly interest rate.
Monthly interest rate = Loan amount × Monthly interest rate
Monthly interest rate = $225,000 × 0.02 = $4,500

Step 3: Calculate the total number of months in the first two years. Since it's a 30-year mortgage, the first two years consist of 24 months.

Step 4: Use the loan amount, monthly interest rate, and number of months in the first two years to calculate the monthly payment using the mortgage payment formula:
Monthly payment = P × r × (1 + r)^n / ((1 + r)^n - 1)
where P is the loan amount, r is the monthly interest rate, and n is the number of months.

Monthly payment = 225,000 × 0.02 × (1 + 0.02)^24 / ((1 + 0.02)^24 - 1)

Calculating this equation gives us the monthly mortgage payment for the first two years.

To calculate the mortgage payments after the second year, we need to find the monthly payment based on the 8.5 percent APR interest rate.

Step 5: Convert the APR interest rate to a monthly rate.
8.5% / 12 = 0.0708 or 0.07 (rounded to two decimal places)

Step 6: Calculate the monthly interest rate by multiplying the loan amount by the monthly interest rate.
Monthly interest rate = $225,000 × 0.07 = $15,750

Step 7: Calculate the total number of months remaining in the mortgage after the second year. Since it's a 30-year mortgage and the first two years already passed, there are 30 - 2 = 28 years remaining, or 28 × 12 = 336 months.

Step 8: Use the loan amount, monthly interest rate, and number of months remaining to calculate the monthly payment using the mortgage payment formula mentioned earlier.

Monthly payment = 225,000 × 0.07 × (1 + 0.07)^336 / ((1 + 0.07)^336 - 1)

Calculating this equation gives us the monthly mortgage payment after the second year.

Please note that the calculations mentioned above do not include property taxes, insurance, or other additional costs associated with the mortgage.