The monthly principal and interest payment is M = P × [i(1+i)^n] / [(1+i)^n − 1]. P is the price minus the down payment. For a United States fixed mortgage, i is the annual rate divided by 12, and n is the number of months. A 30-year loan uses 360 months. The payment stays the same each month. Early payments are mostly interest. Later payments retire more principal.
A $450,000 home with $90,000 down leaves a $360,000 loan. At 6.2% for 30 years the payment is $2,204.89 a month. Interest over the full 360 payments is $433,759.79. The same loan at 15 years is $3,076.92 a month.
Property tax, homeowners insurance, mortgage insurance, and HOA dues are not in the payment. The rate is compounded monthly, which is the US fixed-rate convention. This is not a lender approval and it does not apply Canadian semi-annual compounding. Use the Canada mortgage page for that schedule.