The amount of the mortgage is the difference between the purchase price and the down payment:
$750,000 - $250,000 = $500,000
The monthly interest rate is the annual interest rate divided by 12:
5.50% / 12 = 0.0045833
The number of monthly payments is the number of years times 12:
25 years x 12 months/year = 300 months
Using the formula for the monthly payment of a mortgage, we get:
M = P[r(1+r)^n]/[(1+r)^n - 1]
where:
M = monthly payment
P = principal (amount of mortgage)
r = monthly interest rate
n = total number of payments
Substituting the values we get:
M = $500,000[0.0045833(1+0.0045833)^300]/[(1+0.0045833)^300 - 1] = $2,905.87
Therefore, your monthly payment will be $2,905.87.
The total amount of interest paid over the next 25 years is the total amount of payments minus the principal:
Total interest = M x n - P = $2,905.87 x 300 - $500,000 = $572,722.60
Therefore, the total amount of interest you pay over the next 25 years is $572,722.60.