A 30-year mortgage is the largest amortization schedule most people ever sign — yet lenders quote it as a single monthly number. This guide opens the black box: the payment formula, the full PITI stack, and the prepayment math that quietly saves five figures.
1. Amortization: Same Payment, Different Anatomy Every Month
A fixed-rate mortgage holds the monthly payment constant for 30 years, but the composition of that payment changes every single month. Interest is always charged on the outstanding balance, so the early payments are almost all interest and the late ones almost all principal.
// Monthly payment (fully amortizing, fixed rate)
M = P * r(1+r)^n / ((1+r)^n - 1)
// P = principal, r = annual rate / 12, n = months
//
// Each month then re-splits:
// interest = balance * r
// principal = M - interest
// balance -= principalOn a $360,000 loan at 6.8% for 30 years, the payment is $2,347. Month one splits it into $2,040 interest and $307 principal — 87% of your money services debt, 13% builds equity. The principal share does not cross 50% until around payment 234 (year 19.5). That is not a bank conspiracy; it is what "constant payment on a shrinking balance" mathematically requires.
Amortization Table GeneratorThe full payment-by-payment schedule with running balance, exportable to CSV — watch the interest/principal crossover with your own numbers.→2. PITI: Your Real Payment Has Four Layers
Lenders advertise principal + interest (P&I). Your bank account experiences PITI:
- Principal + Interest — the amortized loan payment from the formula above.
- Taxes — property tax, typically 0.5–2.5% of home value per year depending on state, escrowed monthly.
- Insurance — homeowner’s insurance, roughly $1,500–$3,500/year for a median home, also escrowed.
- PMI — private mortgage insurance, 0.5–1% of the loan per year, charged whenever your down payment is under 20%.
On a $400,000 purchase with 10% down, P&I might be $2,347 while PITI lands near $3,050 — the escrow layers add roughly 30%. Affordability calculators that ignore taxes, insurance, and PMI are not optimistic; they are wrong.
Mortgage Calculator (Full PITI)P&I plus taxes, insurance, and automatic PMI under 20% down — the number your bank account will actually see.→3. Prepayment: The Five-Figure Lever Hiding in the Schedule
Every extra dollar you pay goes directly to principal, and every future interest charge is computed on the now-smaller balance. The effect compounds forward: on that $360,000 loan at 6.8%, adding $200/month cuts the term by roughly 6 years and saves about $92,000 in interest. A single $10,000 lump sum in year 2 still saves around $28,000.
Two disciplines matter more than the amount. First, earlier beats bigger: an extra payment in year 2 saves far more than the same payment in year 20, because it kills decades of future interest. Second, designate the payment: write "apply to principal" on the memo line or the servicer may credit it as next month’s payment — same cash, no interest benefit.
The biweekly trick works on the same principle: 26 half-payments equal 13 monthly payments per year, so one full extra payment sneaks in annually without any budgeting pain.
4. Down Payment: 20% Is a PMI Threshold, Not a Moral Virtue
The 20% rule exists because PMI disappears at 78–80% loan-to-value. But waiting years to save 20% while prices and rents rise has its own cost. The honest comparison runs both paths: a 5% down payment today with PMI versus 20% down three years later with three more years of rent paid.
PMI typically costs 0.5–1% of the loan per year ($150–$300/month on a $360,000 loan) and — the part people miss — it automatically terminates once you reach 78% LTV on the original schedule, and you can request removal at 80%. Paying PMI for 4 years to stop paying rent for 4 years is often the winning trade.
Down Payment CalculatorCompare down-payment tiers against PMI cost and monthly payment — find the tier where the trade actually flips.→5. Rent vs Buy: Find Your Crossover Year
Buying front-loads enormous friction: closing costs of 2–5% to buy, agent commissions around 5–6% to sell. Amortization adds insult — in the first 5 years of a 30-year loan, barely 15% of your payments built equity. If you sell before the crossover, you paid landlord-grade money and the transaction friction.
In most U.S. metros the cumulative rent-vs-buy curves cross around year 5–8; in cheap markets, year 2–3. The crossover moves with three levers: price-to-rent ratio, mortgage rates, and how long you actually stay. Run the curves before falling in love with a listing.
Rent vs Buy CalculatorCumulative renting cost vs net ownership cost plotted year by year — the crossing point answers the question honestly.→The Five-Minute Pre-Signing Checklist
- Compute full PITI, not the advertised P&I — if the lender’s number is 25%+ below yours, you are missing escrow layers.
- Open the amortization schedule and look at month 1: the interest share will make you respect prepayments.
- Test +$100/+$300/+$500 extra per month and pick the tier you can sustain — consistency beats heroics.
- Check the crossover year against your realistic plan to stay — not your optimistic one.
- Verify every figure runs in your browser with no sign-up — your loan amount is nobody else’s data.