Editorial guide
A mortgage looks like a single monthly number, but it's really three intertwined decisions: how much you borrow, how long you stretch it, and what price you pay for the money. Get any one wrong and the other two work against you for decades. This guide unpacks the maths lenders use, shows what a 15-year versus 30-year choice actually costs, and gives the affordability rules professionals apply before they approve a loan.
How mortgage payments are calculated
Every fixed-rate, fully amortizing mortgage, the standard in the US and the model for UK repayment mortgages, uses one formula to turn a lump-sum loan into equal monthly instalments:
M = P · r · (1+r)n / ((1+r)n − 1)
- P: principal - home price minus down payment. $400,000 price with 20% down ($80,000) gives P = $320,000. This is the only input that is not a rate or time.
- r: monthly rate - annual APR divided by 12. A 6.50% APR means r = 0.065 / 12 = 0.0054167, about half a percent per month. That tiny monthly slice is what compounds.
- n: total payments - years × 12. Thirty years is 360 cheques; 15 years is 180. Doubling term does not halve the payment, because interest has more months to accrue.
- M: monthly principal & interest (P&I). Taxes, insurance, HOA and PMI sit on top in the real world; this formula is strictly debt service to the bank.
For the example above: r = 0.0054167, n = 360, (1+r)ⁿ ≈ 7.04. Then M = 320,000 × 0.0054167 × 7.04 / (7.04 − 1) ≈ $2,022. The first cheque splits as roughly $1,733 interest (320,000 × r) and $289 principal. By month 180, interest has fallen to about $1,060 and principal risen to $962, same M, but the mix has inverted. That front-loading is why extra payments early are so powerful: they cancel the most expensive interest tail.
Total interest is simply M × n − P. Here $2,022 × 360 − $320,000 ≈ $408,000 of interest, more than the house borrowed, which surprises first-time buyers but is the normal shape of a long, moderate-rate loan. The bar chart above makes this vivid: in year one each bar is mostly amber (interest), and the dark principal slice grows month by month. The donut condenses the whole loan into two wedges: principal you keep as equity, interest you pay for the privilege of time.
Three subtleties matter if you reconcile the calculator to a lender truth-in-lending disclosure: (1) we compound monthly, as US mortgages do, and assume each payment lands on schedule with no intra-month daily accrual; (2) we amortize on a 12-month year with no odd-days interest; (3) we apply any extra payment wholly to principal the same month, which is how servicers must apply it if you label it “principal only.” Those assumptions put us within dollars of Loan Estimate tables for standard conforming loans.
15 vs 30 year comparison table
Term is the biggest lever after price. The trade is always the same: fewer years, higher monthly obligation, dramatically less lifetime interest and sooner ownership. The table fixes price at $400,000, down 20% (P = $320,000) and two realistic rates: 6.00% for 15-year, 6.50% for 30-year (shorter terms price tighter). Extra payments are zero so the contrast is pure term and rate.
| Term | Rate | Monthly P&I | Total interest | Total paid |
|---|---|---|---|---|
| 15 years | 6.00% | $2,701 | $166,178 | $486,178 |
| 20 years | 6.25% | $2,339 | $241,360 | $561,360 |
| 25 years | 6.50% | $2,160 | $328,000 | $648,000 |
| 30 years | 6.50% | $2,022 | $407,920 | $727,920 |
| 30 years + $300 extra | 6.50% | $2,322 | $263,040* | $583,040* |
*With $300 extra to principal from month one, payoff drops from 360 to ~236 months (~19.7 years), interest saved ≈ $145k. Figures rounded, P&I only, monthly compounding.
Two patterns jump out. First, monthly cost is not proportional to term: doubling from 15 to 30 years cuts the payment by only 25%, because you pay for 15 more years of interest. Second, the last row is the arbitrage most households miss: a 30-year priced as a 30-year but paid like a 25-year keeps the lower contractual obligation, you can fall back to $2,022 if income dips, yet captures $145k of the 15-year's interest saving when times are good. Discipline, not contract, creates that hybrid.
Lenders also price this: the 15-year’s 6.00% vs 30-year 6.50% reflects a lower term premium and credit risk. Even 0.5% matters. On $320k, 6.00% vs 6.50% over 30 years is $110 less a month and $40k less interest. Lock comparisons must be same-day; rate markets move more in a week than the term spread does in a year.
How much house can you afford rule
Underwriting and budgeting answer “how much house” differently. Underwriting asks if the bank is safe; budgeting asks if you are comfortable. Both use debt-to-income (DTI), but the sensible answer is the tighter of the two.
The 28/36 rule (US benchmark). Housing expense (PITI + HOA + PMI) should be ≤28% of gross monthly income, and all recurring debt (housing + auto + student loans + minimum cards) ≤36%. At $90,000 gross ($7,500/mo), 28% is $2,100 for housing total. If taxes are $350, insurance $150 and HOA $200, your P&I ceiling is about $1,400, which at 6.5%/30yr buys roughly $220k of loan, or a $275k price at 20% down. That often surprises dual-income households who anchor on combined income; lenders use gross, but you should test against take-home, where $2,100 is a much larger share.
The 3× income / 35% take-home cross-check (UK + US budgeting). A quick planner’s test is price ≤ 3–4.5× gross income (UK lenders cap near 4.5×) and mortgage payment ≤25–35% of after-tax pay. At £60,000 gross (£3,700 net in England, ~£44k net after tax/NI/pension), 35% of net is £1,295, at 5.0%/25yr that services about £220k of loan, £275k at 20% down. If the 3× and the 35% tests disagree, trust the take-home one; gross multiples ignore student loans and region-specific payroll taxes.
Practical guardrails we recommend in the calculator workflow: (1) run once on gross for lender DTI, once on net for lifestyle; (2) stress the payment at +2% rate, can you still cover it if you refinance later is not an option; (3) add a vacancy or repair buffer if you buy at the top of approval, a boiler in month four should not force a credit card at 24% APR while you service a mortgage at 6.5%. Affordability is not the maximum the bank offers; it is the level where a 10% income dip or a £/ $5k repair does not break the budget.
Down payment impact
Down payment moves three dials at once: loan size, price of credit, and equity cushion. The non-linear jump is at 20%.
Take the same $400,000 price at 6.50% / 30 years:
- 10% down ($40,000): P = $360,000, LTV 90%, M ≈ $2,275, total interest ≈ $459k. You likely pay PMI (private mortgage insurance), say 0.6% of loan annually (~$180/mo) until you hit 80% LTV, and you start with only 10% equity, so a 5% price dip puts you near underwater on sale after costs.
- 20% down ($80,000): P = $320,000, LTV 80%, M ≈ $2,022, total interest ≈ $408k. No PMI, $253 less P&I than the 10% case, plus the $180 PMI saving, $433/mo cheaper to own, and you keep a 20% buffer against a downturn.
- 30% down ($120,000): P = $280,000, LTV 70%, M ≈ $1,770, total interest ≈ $357k. Only $252 less than the 20% case; the PMI saving is already captured, so the marginal benefit is straight debt reduction. For some buyers the extra $40k down is better kept as a 6–9 month emergency fund or to clear 20% APR debt first.
The UK parallel is stamp duty thresholds and LTV bands: a 10% deposit buys access but at a higher LTV rate tier (often +0.4–0.7% above 60% LTV products), while 25–40% down qualifies for the cheapest rates. Across both markets the lesson is consistent: clear the 20% (or the lowest fee tier) if you can without gutting liquidity, then stop. Every extra point beyond that earns the mortgage rate as a return (you avoid 6.5% interest), which is risk-free but illiquid, selling to reclaim it costs months and ~2–6% in transaction fees.
Down payment also interacts with extra payments. A buyer who can only put 10% down but can add $300/mo extra is in effect building the missing down payment after purchase: the extra retires principal at the contract rate, kills PMI faster (request removal at 80% LTV by appraisal), and shortens the high-cost early phase. The calculator's payoff date moves as you raise down percent, watch the "LTV" helper; when it drops through 80%, price that PMI deletion into the true monthly cost.
Methodology and assumptions
We publish assumptions so a broker, a spreadsheet and this tool can be reconciled to the dollar. Every figure on this page comes from the live calculator above; there is no server-side estimate.
- Product: Fixed-rate, fully amortizing, monthly compounding, level payments. Not interest-only, not ARM, not offset.
- Scope: P&I only. Excludes property tax, homeowner’s insurance, HOA dues, PMI, origination fees, points, and prepayment penalties. Add those from your Loan Estimate to compare lenders apples-to-apples.
- Formula: M = P·r·(1+r)ⁿ/((1+r)ⁿ−1) with r = APR/12, n = years×12, P = price × (1 − down %). Total interest = Σ interest per month; total paid = P + total interest. Rounding per payment to cents, balance floored at $0.
- Extra payments: Applied 100% to principal in the month paid, reducing the balance before next month’s interest accrues. No lag, no “held as advance payment.” If your servicer holds extra as a credit, results will lag by one month.
- Schedule: Month 1 balance is P. Interest = balance × r. Principal = min(balance, M − interest + extra). Balance is decremented; loop stops when ≤$0.01. The table shows months 1–12 plus the final row; the full schedule length is actualMonths.
- Payoff date: Today plus actualMonths calendar months via date arithmetic; does not account for the loan’s actual closing date. Add closing-to-first-payment gap for exact maturity.
- Range limits: Price $100k–$1M, down 0–50%, APR 2–10% step 0.1, term 15/20/25/30. Extrapolation beyond uses the same maths but lender pricing outside those bands differs.
- What would change a disclosure: Daily simple-interest accrual, bi-weekly compounding, upfront points (prepaid interest), seller concessions, buydowns, and tax escrow timing all shift the lender’s APR from the note rate. This tool shows note-rate economics so you can price the deal before fees; the APR on your disclosure will be slightly higher once fees amortize.
If statutory guidelines change, our code is updated with a transparent changelog. Bookmark your inputs: re-running the same parameters will reproduce identical P&I calculations.