Answer:
M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1]
where M is the monthly payment, P is the principal (the cost of the house minus the down payment), i is the monthly interest rate (6.00% divided by 12), and n is the total number of payments (30 years times 12 months per year).
Plugging in the values, we get:
P = $450,000 - 0 (assuming no down payment)
i = 0.06 / 12 = 0.005
n = 30 x 12 = 360
M = $450,000 [ 0.005(1 + 0.005)^360 ] / [ (1 + 0.005)^360 - 1] = $2,695.55
So the monthly mortgage payment is $2,695.55.
To find the monthly payment with taxes and insurance, we need to add the yearly taxes and insurance and divide by 12 to get the monthly amounts. So:
Monthly Taxes = $2,000 / 12 = $166.67
Monthly Insurance = $1,500 / 12 = $125.00
Total Monthly Payment with Taxes and Insurance = $2,695.55 + $166.67 + $125.00 = $2,987.22
Therefore, the monthly payments with taxes and insurance for the $450,000 house loan are $2,987.22.