Final answer:
The monthly payments for the first three years of the mortgage, with a buy-down contract rate of 5% for the first year and 6.5% for the second year, are $1,496.15 for Year 1, $1,756.36 for Year 2, and $2,287.89 for Year 3.
Step-by-step explanation:
To calculate the payments for the first three years, we need to calculate the monthly payment for the mortgage at each interest rate. We can use the formula for calculating the monthly payment on a mortgage:
Monthly Payment = P * r * (1 + r)n / ((1 + r)n - 1)
Where:
Let's plug in the values for each year:
Year 1:
Principal Amount (P) = $265,000
Monthly Interest Rate (r) = 5% / 12 = 0.4167
Number of Monthly Payments (n) = 30 * 12 = 360
Monthly Payment for Year 1 = $265,000 * 0.4167 * (1 + 0.4167)360 / ((1 + 0.4167)360 - 1) = $1,496.15
Similarly, we can calculate the monthly payments for Year 2 and Year 3 using the same formula:
Year 2:
Principal Amount (P) = $265,000
Monthly Interest Rate (r) = 6.5% / 12 = 0.5417
Number of Monthly Payments (n) = 28 * 12 = 336
Monthly Payment for Year 2 = $265,000 * 0.5417 * (1 + 0.5417)336 / ((1 + 0.5417)336 - 1) = $1,756.36
Year 3:
Principal Amount (P) = $265,000
Monthly Interest Rate (r) = 8.5% / 12 = 0.7083
Number of Monthly Payments (n) = 12 * 12 = 144
Monthly Payment for Year 3 = $265,000 * 0.7083 * (1 + 0.7083)144 / ((1 + 0.7083)144 - 1) = $2,287.89