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Monthly payment = P × [r(1+r)^n] / [(1+r)^n − 1], where P = principal, r = monthly interest rate (annual rate ÷ 12), n = number of monthly payments. Example: $200,000 loan at 6% for 30 years → r = 0.005, n = 360 → Monthly payment = $1,199.10. This formula gives equal payments throughout the loan term (fully amortizing loan). The payment stays constant, but the proportion going to principal vs. interest shifts each month.

Amortization is the process of paying off a loan through regular payments that cover both principal and interest. In the early months, most of each payment goes toward interest. As the balance decreases, more goes toward principal. Example: on a $200k 30-year mortgage at 6%, month 1 payment of $1,199: $1,000 interest, $199 principal. Month 180: ~$700 interest, ~$499 principal. Month 360: ~$6 interest, ~$1,193 principal. Total interest over 30 years: ~$231,676 — more than the original loan!

Even small rate differences have huge long-term impact. Example $300,000 loan for 30 years: At 5%: monthly $1,610, total interest $279,767. At 6%: monthly $1,799, total interest $347,515. At 7%: monthly $1,996, total interest $418,527. A 1% rate increase on a $300k mortgage costs ~$68k more in interest over 30 years. This is why refinancing when rates drop can save tens of thousands of dollars.

Interest rate: the cost of borrowing the principal, expressed as a percentage per year. APR (Annual Percentage Rate): includes interest rate PLUS fees (origination fees, points, mortgage insurance). APR reflects the true annual cost of the loan. Example: a loan with 6% interest rate but $3,000 in fees on a $200k loan has an APR of ~6.15%. By law (TILA), lenders must disclose APR. When comparing loans, use APR to make an apples-to-apples comparison since it includes all costs.

15-year mortgage: higher monthly payment, much lower total interest, builds equity faster. 30-year mortgage: lower monthly payment (easier to afford), more total interest paid, flexibility (can pay extra principal voluntarily). Example: $300k at 6%. 15-year: $2,532/month, total interest $155,682. 30-year: $1,799/month, total interest $347,515. The $733/month savings from 30-year could be invested — at 7% return, $733/month for 15 years = ~$228k. The 30-year may actually come out ahead if you invest the difference.