The Mortgage Payment Formula
The standard fixed-rate mortgage formula calculates a level monthly payment that retires the loan exactly at the end of the term:
M = P × [r(1 + r)ⁿ] ÷ [(1 + r)ⁿ − 1]
Where M = monthly payment, P = loan principal (home price minus down payment), r = monthly interest rate (annual rate ÷ 12), and n = total number of payments (years × 12).
Example: $400,000 home, 20% down ($80,000), 30-year term, 7.0% annual rate. P = $320,000, r = 0.005833, n = 360. Monthly payment = $2,129. Total paid: $766,440. Total interest: $446,440.
How Extra Payments Reduce Total Interest
Each extra dollar paid toward principal reduces the outstanding balance, which directly reduces future interest charges. Because interest compounds monthly on the remaining balance, extra payments applied early in the loan have a disproportionately large effect.
Example: On the $320,000 loan above (30-year at 7%), adding $300/month extra cuts the payoff to roughly 22 years and saves approximately $120,000 in interest. The savings are largest when the extra payment starts early, because the balance — and therefore the monthly interest charge — is at its peak.
How Down Payment Affects the Loan
Down payment directly reduces the loan principal, which reduces the monthly payment and total interest. It also determines whether private mortgage insurance (PMI) applies.
Lenders generally require PMI when the down payment is below 20% of the purchase price. PMI typically costs 0.5%–1.5% of the loan amount annually, added to the monthly payment until the loan-to-value ratio drops to 80%. On a $400,000 home with 10% down, PMI might add $125–$375/month.
The calculator estimates when PMI drops off based on the amortization schedule reaching 80% LTV — this is an estimate only; actual drop-off depends on lender policy and may require a formal request.
Loan Term and Interest Rate: How They Interact
A shorter loan term means higher monthly payments but significantly less total interest. A longer term reduces the monthly payment but costs more over the life of the loan.
These figures use a $320,000 loan. The term comparison widget shows all four options side by side after you calculate.
How Amortization Works
Each monthly payment covers interest accrued during the period plus a portion of principal. In the early years of a mortgage, most of each payment is interest — this is called front-loaded amortization.
On a $320,000 loan at 7% (30-year), the first payment of $2,129 breaks down as: Interest $1,867, Principal $262. By year 15, roughly half goes to principal. The annual amortization schedule below the calculator shows exactly how much interest and principal you pay each year, plus your running equity percentage.
P&I vs. PITI
This calculator computes P&I (principal and interest), which is the core mortgage payment. Your actual monthly housing cost is typically PITI: principal, interest, property taxes, and homeowners insurance.
Property taxes vary widely by location — typically 0.5%–2.5% of home value annually. Homeowners insurance typically runs $800–$2,500/year. HOA fees, if applicable, are separate and do not go through the lender.