How do you actually calculate mortgage interest from scratch?

The basic formula is monthly interest = (remaining balance × annual rate) ÷ 12, and you apply that to each month's unpaid principal. So if you owe $300,000 at 5% annual interest, your first month's interest is roughly $1,250 - then that gets added to your principal payment to make up your total monthly payment. Over time the interest portion shrinks as your balance drops and more of each payment goes toward principal. Most people just use a calculator or their lender's amortization schedule rather than doing it by hand, since the math gets tedious across 360 payments.