Answer: Rounding the difference to the nearest dollar, the difference in the total cost between the two mortgages is approximately $889,597.
Explanation:
To calculate the difference in the total cost between the adjustable rate mortgage and the fixed-rate mortgage, we need to determine the total payments for each mortgage and find the difference.
For the adjustable rate mortgage, the total payments can be calculated by summing up the monthly payments over the loan term. Based on the given information, we have the following payments:
Year 1: $2,506.43
Year 6-15: $3,059.46
Year 16-25: $3,464.78
Year 26-30: $3,630.65
To calculate the total payments for the adjustable rate mortgage, we add up the payments for each year:
Total payments = Year 1 + Year 6-15 + Year 16-25 + Year 26-30
Total payments = $2,506.43 + ($3,059.46 * 10) + ($3,464.78 * 10) + ($3,630.65 * 5)
Now let's calculate the total payments for the adjustable rate mortgage:
Total payments = $2,506.43 + $30,594.60 + $34,647.80 + $18,153.25
Total payments = $85,902.08
Now, let's calculate the total cost for the fixed-rate mortgage. We'll assume the loan amount is the same as the adjustable rate mortgage, which is $525,000. The interest rate for the fixed-rate mortgage is given as 4.65%.
Using a mortgage calculator or formula, we can determine the monthly payment for the fixed-rate mortgage. Let's calculate it:
Monthly payment = P * r * (1 + r)^n / ((1 + r)^n - 1)
P = $525,000 (loan amount)
r = 4.65% (interest rate per period)
n = 30 (loan term in years)
Monthly payment = $525,000 * (0.0465/12) * (1 + (0.0465/12))^360 / ((1 + (0.0465/12))^360 - 1)
Calculating the above expression, we find that the monthly payment for the fixed-rate mortgage is approximately $2,709.72.
To calculate the total payments for the fixed-rate mortgage, we multiply the monthly payment by the number of months (360):
Total payments = $2,709.72 * 360
Total payments = $975,499.20
Finally, we can find the difference in the total cost between the two mortgages:
Difference = Total payments (Fixed-rate mortgage) - Total payments (Adjustable rate mortgage)
Difference = $975,499.20 - $85,902.08
Difference = $889,597.12