What is Mortgage Calculator?
How It Works
You enter the purchase price and down payment percentage; we compute the loan amount and starting LTV. The interest rate and term set your fixed principal-and-interest payment using monthly compounding consistent with common U.S. mortgage quotes. Annual property tax and insurance are divided by twelve to show a monthly escrow-style amount. HOA is already a monthly fee. If LTV at closing exceeds 80%, we add PMI using your annual PMI rate as a percent of the original loan balance, spread monthly. Month by month we accrue interest on the remaining balance, reduce principal, and stop PMI once the balance reaches 78% of the original home price in this model. A yearly summary table aggregates principal, interest, PMI paid, and ending balance.
Formula
Monthly P&I (fixed rate): M = P × r × (1 + r)^n / ((1 + r)^n − 1) P = loan amount, r = annual rate / 12 / 100, n = months Monthly escrow-style: tax_month = annual_property_tax / 12 ins_month = annual_home_insurance / 12 PMI (while active, conventional-style estimate): pmi_month ≈ (P × PMI_annual_%) / 12 until remaining principal ≤ 0.78 × original purchase price
Formula Explained
The P&I formula is the standard closed-form solution for a fully amortizing installment loan: the payment M is chosen so that after n months the balance is exactly zero if every payment is made on time at the stated rate. Property tax and insurance are not “interest” — they are ongoing housing costs often paid monthly through an escrow account; we show them as monthly equivalents by dividing annual figures by twelve. PMI is not computed like interest on the declining balance in this simplified model; many PMI quotes are stated as an upfront annual rate on the original loan amount until cancellation criteria are met. That is why we hold the monthly PMI flat until the modeled removal point, then drop it — a reasonable first approximation for budgeting.
Example
Purchase price $400,000, 10% down → loan $360,000, LTV 90%. 30-year fixed at 6.75% annual → monthly P&I is computed from the amortization formula (order of hundreds of dollars depends on exact rounding). If annual PMI is 0.75% of the original loan, monthly PMI ≈ (360,000 × 0.0075) / 12 = $225 until the balance reaches 78% of $400,000 ($312,000). Each month, interest is charged on the remaining balance and principal is reduced until that threshold is crossed; then PMI goes to zero in the model while P&I and escrow continue.
Tips & Best Practices
- ✓Compare APR and total interest over the loan, not only the monthly payment.
- ✓Property tax and insurance change — reassess annually when you budget.
- ✓If you can reach 20% down, you may avoid PMI entirely on many conventional loans.
- ✓Shorter terms (15-year) raise monthly P&I but cut total interest sharply.
- ✓Keep an emergency fund beyond the down payment for repairs and vacancies.
Common Use Cases
- •Sizing a monthly housing budget before talking to lenders
- •Seeing how down payment changes PMI and total monthly cost
- •Comparing 15-year vs 30-year total interest
- •Explaining PITI to first-time buyers
- •Rough what-if scenarios when rates move