Final answer:
The total cost of the home with a 15-year mortgage is $472,728.40, and with a 30-year mortgage, it's $617,682.40, both including the $51,500 down payment.
Step-by-step explanation:
To calculate the total cost of the home including the down payment, we add the initial down payment to the total amount paid over the course of the mortgage. For a 15-year fixed mortgage at a monthly payment of $2,336.83, the total paid for the loan is $2,336.83 multiplied by 12 months per year and then by 15 years, plus the down payment.
Down Payment: $51,500.00
Total Monthly Payments: $2,336.83 x 12 x 15 = $421,228.40
Total Cost of Home: $421,228.40 + $51,500.00 = $472,728.40
Similarly, for a 30-year fixed loan at a monthly payment of $1,573.84:
Total Monthly Payments: $1,573.84 x 12 x 30 = $566,182.40
Total Cost of Home: $566,182.40 + $51,500.00 = $617,682.40