Formulas, methodology and assumptions

Fixed-rate amortizing payment

Let L be principal, r the monthly rate (annual percentage divided by 1,200), and n the number of monthly payments. The payment is M = L × r ÷ [1 − (1 + r)⁻ⁿ]. For a zero interest rate, M = L ÷ n. We use the stated annual note rate, not APR, for scheduled principal and interest.

Each month’s interest is beginning balance × monthly rate. Principal paid equals scheduled payment minus that interest. The new balance equals beginning balance minus principal paid. We clamp the final payment to avoid tiny negative balances caused by floating-point rounding.

Housing cost and down payment

Loan principal = home price − down payment. Estimated monthly housing cost = principal-and-interest payment + annual property tax ÷ 12 + annual insurance ÷ 12 + monthly HOA + monthly PMI. The calculator does not estimate taxes or insurance automatically because both vary by location, property, and insurer.

Extra payments

For the extra-principal simulation, we recalculate interest on each remaining balance and apply the regular payment plus the extra amount to the loan. We stop when the balance reaches zero. Savings equal interest from the original schedule minus interest from the accelerated schedule. We assume the additional amount goes to principal, begins immediately, and remains constant.

Refinance break-even and points

Simple refinance break-even months = closing costs ÷ (old monthly principal-and-interest payment − new monthly principal-and-interest payment), when savings are positive. This metric assumes the same remaining term for both loans and ignores the time value of money, taxes, escrow, and changes in mortgage insurance.

Point cost = loan principal × points percentage ÷ 100. Simple point break-even months = point cost ÷ monthly payment savings, when savings are positive. The rate difference must come from real competing quotes; we do not invent a points-to-rate conversion.

Debt-to-income ratio

Housing DTI = estimated monthly housing cost ÷ gross monthly income × 100. Total DTI = (housing cost + other monthly debt) ÷ gross monthly income × 100. These are educational ratios, not qualification determinations. Actual underwriting may count income, debts, and expenses differently.

Limitations and rounding

Calculations assume fixed nominal annual rates compounded monthly, regular monthly payments, no delinquency, and no mid-term rate changes. They do not calculate APR, taxes on mortgage interest, ARM resets, escrow changes, lender credits, upfront mortgage insurance, or closing disclosure totals. Results are rounded for display but computed at higher precision internally. Confirm all amounts with the lender and closing documents.