Mortgage Calculation: Understanding the Numbers Behind Your Loan
A mortgage is the largest debt most people take on. After buying my first home, I learned what the numbers actually mean. Buying a home meant taking on the largest debt of my life. The monthly payment, the interest, the amortization schedule, all of it felt abstract until I ran the numbers myself. Understanding the math behind a mortgage helped me compare offers, choose a term, and decide whether to refinance. Here is, with the calculations I use and the mistakes I avoided by doing the math before signing. The Monthly Payment Formula The monthly payment on a fixed-rate mortgage is calculated from the loan amount, the monthly interest rate, and the number of payments. The formula is M equals P times r times one plus r to the n, divided by one plus r to the n minus one. P is the principal, r is the monthly rate, and n is the total number of payments. M = P * r * (1 + r)^n / ((1 + r)^n - 1) P = principal (loan amount) r = monthly interest rate (annual rate / 12) n = total number of payments (years * 12) M = monthly payment For a 300,000 dollar loan at 6 percent annual interest for 30 years: P is 300000, r is 0.005, and n is 360. The monthly payment is about 1,798 dollars for principal and interest.