Calculation methodology

This page documents the arithmetic behind every calculator on Mortgage Ledger: the formulas, the compounding and rounding conventions, the assumptions baked into each tool, and — just as importantly — what each tool leaves out. It is written so that a reader can reproduce any result here by hand and check it.

If a figure on this site does not reconcile with your lender's, the cause is almost always an assumption rather than an error. This page is where the assumptions are.

Every calculator on this site derives a fixed monthly payment from the standard amortizing-loan formula:

The schedule is built one month at a time. For each period, in this order:

1. Interest accrues on the balance actually outstanding: interest = balance × r.
2. The remainder of the fixed payment reduces principal: principal = M − interest.
3. Any extra principal is applied on top (see section 5).
4. The balance is reduced by principal plus extra, and the next month accrues interest on that smaller balance.

This is why the split moves: the payment is constant, but as the balance falls, the interest share falls with it and the principal share grows to fill the gap. It is also why extra principal compounds — every dollar removed from the balance today removes interest from every month that follows.

Continuing the example above, the first month on a $400,000 loan at 6.5% accrues $400,000 × 0.0054166 = $2,166.67 of interest, leaving $2,528.27 − $2,166.67 = $361.60 to principal. Only 14% of the first payment touches the debt.

The crossover month reported by the main calculator is the first month in which cumulative principal paid to date exceeds cumulative interest paid to date. It is a plain-English marker, not a lending term.

The schedule terminates when the balance reaches zero (specifically, when it falls below half a cent). A final payment is trimmed so the loan cannot overshoot into a negative balance.

• Monthly compounding. Interest is compounded and charged monthly, which is the convention for standard US fixed-rate mortgages.
• The periodic rate is the annual rate divided by 12 — a nominal annual rate, not an effective one. We do not convert to an effective annual rate, because lenders do not.
• Every month is treated as equal. The calculators use a fixed 12-period year and do not model actual day counts, so February and July are treated identically. Most US mortgages are indeed 30/360-style for payment purposes, but a lender that accrues interest on actual days may differ from this site by a few dollars in a given month.
• Payments are assumed to be made on time, in full, on the scheduled date. No late fees, grace periods, or partial payments are modeled.
• The rate is assumed fixed for the entire term. No calculator on this site models an adjustable-rate mortgage, a rate reset, an interest-only period, a balloon, or negative amortization.

This is a common source of small discrepancies against a lender's schedule, so it is worth being precise.

• Internally, nothing is rounded. The payment, the interest, the principal, and the running balance are all carried at full floating-point precision through the entire schedule. Rounding happens only at the moment a number is displayed.
• Displayed figures are rounded to the nearest cent for payments and to the nearest dollar for large totals such as total interest.
• Lenders do the opposite. A servicer typically rounds the monthly payment to the cent and then amortizes that rounded figure, carrying the rounding difference through the schedule and absorbing it in a slightly adjusted final payment.

The practical consequence: over a 360-month schedule, this site and your servicer may differ by a few dollars in total interest, and your final payment may be a slightly different size than the one shown here. This is a rounding artifact, not a disagreement about the loan. Treat every figure here as a close estimate for planning, never as a reconciliation of your actual account.

• Extra payments are applied entirely to principal, in the same period they are made, after that month's interest has been charged.
• The required monthly payment does not change. Extra principal shortens the loan; it does not re-amortize it. To reduce the required payment you need a refinance or a recast.
• Both a recurring monthly extra and one-time extras in specific months are supported; where both are present in a month, they are summed.
• The extra is capped so the balance cannot go below zero. In the final month, only what is needed to clear the loan is applied.
• Interest saved is computed by building a second, independent schedule for the identical loan with no extra payments at all, and differencing the two totals. It is a true like-for-like comparison, not an approximation.

The refinance calculator compares what is left of your current loan against a proposed new loan.

• The current payment is reconstructed from your remaining balance, your current rate, and your remaining years — not your original term. This is the correct comparison: what matters is the obligation you have left, not the one you started with.
• The new loan principal is the current balance, plus closing costs if you choose to finance them.
• Simple monthly saving = old payment − new payment.
• Simple breakeven = closing costs ÷ monthly saving, rounded up to the next whole month.
• Lifetime difference = (old payment × old months remaining) − (new payment × new months + any cash paid at closing). This is what catches the trap below.

Financed closing costs vs. cash at closing. If you pay costs in cash, that cash is a real outlay and the breakeven measures how long it takes to earn it back. If you roll costs into the loan, there is no cash outlay — but you now borrow more, and you pay interest on those costs for the entire new term. The breakeven figure shown is the simple one (costs ÷ monthly saving) in both cases; the true cost of financing them is captured in the lifetime-difference line, which is the figure to trust.

What the refinance calculator does not account for:

• Taxes. Mortgage interest is deductible only if you itemize, and only within the acquisition-debt limit. A refinance that cuts your interest also cuts your deduction, so the after-tax saving is smaller than the pre-tax saving for anyone who itemizes. Points paid on a refinance generally must be deducted over the life of the loan rather than in the year paid. None of this is modeled.
• Escrow. Taxes and insurance are not included; a refinance re-establishes escrow, and you may pay into a new escrow account at closing while your old one is refunded. This is a cash-flow event, not a cost, and is not modeled.
• Mortgage insurance changes, cash-out amounts, prepayment penalties, and the opportunity cost of the cash spent at closing.
• Whether you will actually keep the loan past the breakeven month. If you sell or refinance again first, the closing costs are simply lost.

The rent-versus-buy calculator computes a net cost for each path over your chosen horizon and compares them. It is a cost comparison, not a lifestyle one.

The buyer's net cost accumulates, year by year:

• Upfront: the down payment plus buying/closing costs (a percentage of price).
• Every mortgage payment made (principal and interest both count as cash out).
• Property tax, charged as a percentage of the home's current, appreciated value each year.
• Homeowners insurance (a flat annual figure).
• Maintenance, as a percentage of current value each year.
• HOA dues.

From that total it subtracts net sale proceeds at the horizon: the appreciated value, less selling costs as a percentage, less the remaining loan balance. The result is what owning actually cost you, after you get out.

The renter's net cost accumulates rent paid, with rent growing by the annual rent-increase rate each year, and subtracts the investment gains on the money the buyer would have tied up at the start (the down payment plus buying costs), compounded at the investment-return rate.

The breakeven year is the first year in which the buyer's cumulative net cost falls at or below the renter's.

Also not modeled: PMI (if you put down less than 20%); the fact that many states cap annual assessed-value growth for property tax, so a tax bill may rise more slowly than the home's market value; insurance premium inflation (the figure is flat); transaction costs of a second move; rent controls; the risk that appreciation is negative; and the fact that both appreciation and investment returns are entered as smooth annual rates when neither is smooth in reality.

The affordability calculator works backwards from income to a price. It caps your monthly housing budget by two ratios and takes the lower of the two:

• Front-end (housing) ratio: housing payment ÷ gross monthly income.
• Back-end (total debt) ratio: (housing payment + all other monthly debt payments) ÷ gross monthly income.

The budget is then solved back into a purchase price, holding the down payment fixed:

What the affordability calculator does not account for: mortgage insurance (if your down payment is under 20%, your real payment will be higher than modeled — the tool warns you but does not add PMI to the math); closing costs, which you must fund on top of the down payment; reserve requirements; credit score, which drives both your rate and your eligibility; the stability or documentability of your income; student-loan payment calculation rules, which differ by loan program for deferred loans; and every non-debt expense in your life.

Where the main calculator estimates PMI removal, it does so on a single, narrow basis: it reports the month in which the scheduled loan balance first falls to 80% of the home value you entered, through payments alone.

That is a useful planning marker, but the real rules are considerably more involved, and the calculator does not model them:

• Under the federal Homeowners Protection Act, for a loan on a single-family primary residence, a borrower may generally request cancellation of borrower-paid PMI when the balance reaches 80% of the original value — the lesser of the purchase price or the appraised value at origination — and the servicer must automatically terminate it at 78% of original value, provided the borrower is current. There is also a final termination at the midpoint of the amortization period.
• The Act's thresholds run off original value, not current market value. Cancellation on the basis of appreciation is not an HPA right at all — it is governed by investor rules (for example Fannie Mae's and Freddie Mac's servicing guides), which impose their own seasoning requirements and generally require a new appraisal or broker price opinion that you pay for.
• Cancellation typically also requires a good payment history, no subordinate liens, and evidence that the property has not declined in value.
• FHA mortgage insurance does not work this way at all. On most current FHA loans with less than 10% down, the annual MIP runs for the life of the loan, and reaching 20% equity does not cancel it — the usual exit is refinancing into a conventional loan. See our guide on how PMI works and when it goes away.
• Lender-paid PMI, single-premium PMI, split-premium PMI, and loans on investment properties or second homes all follow different rules again.

The calculator does not add a PMI premium to your monthly payment; the payment shown is principal and interest only. Nothing on this site is a determination that your PMI can or cannot be cancelled — that determination belongs to your servicer, under your loan's actual terms.

• Property tax is entered as an annual percentage of home value and is charged as such. It is not derived from any assessment roll, mill rate, or local exemption.
• In the rent-versus-buy calculator, tax is charged on the home's appreciated value each year — which will overstate the tax bill in jurisdictions that cap annual growth in assessed value.
• Homestead exemptions, senior or veteran exemptions, assessment caps, reassessment on sale, special assessments, and Mello-Roos-style district levies are not modeled.
• The deductibility of property tax (and the SALT cap that limits it) is not modeled.

Effective property-tax rates vary enormously by state and locality. Use your county assessor's actual figure for the specific property, not a national average.

• Homeowners insurance is entered as a flat annual dollar amount and is held constant across the horizon. It does not inflate, and it does not scale with the home's value.
• This is a simplification, and in the current market it is a generous one to buyers: premiums in many regions have been rising considerably faster than general inflation, particularly where wildfire, wind, flood, or hail exposure is material.
• Flood insurance, earthquake insurance, wind/hail deductibles, and umbrella coverage are not modeled, and flood insurance in particular is a separate policy that can be a large, mandatory addition in a special flood hazard area.
• Insurance is not included in the main mortgage calculator's payment at all — that figure is principal and interest only.

The rent-versus-buy calculator asks you for an annual home appreciation rate and an annual investment return. These are the two most consequential inputs in the entire tool, and they are the two nobody can know.

• Both are applied as smooth, constant, annually compounded rates. Real markets are not smooth; sequence matters enormously, and a fall in the first few years of ownership is far more damaging than the same fall later.
• Investment returns are treated as pre-tax. No capital-gains tax, dividend tax, or drag from fees is applied.
• Home appreciation is applied to the whole property value, which is why leverage makes it so powerful — and why it cuts equally hard in reverse. A 10% fall on a home bought with 10% down does not reduce your equity by 10%; it eliminates it.
• No default value is presented as a forecast. Whatever numbers are preloaded are illustrative starting points, not predictions, and you should change them.

• All figures are estimates for education and planning. None is a loan offer, a rate quote, a pre-qualification, a pre-approval, or a commitment to lend.
• Every tool assumes a fixed rate for the full term. Adjustable-rate mortgages, interest-only periods, balloons, buydowns, and negative amortization are not modeled.
• Fees and points are not modeled unless a tool explicitly asks for them, and no tool computes APR.
• Results depend entirely on the inputs you supply. A precise-looking output built on a guessed input is still a guess — the decimal places are not evidence.
• Your lender's Loan Estimate and Closing Disclosure are the authoritative statements of what a loan will cost you. Where this site and those documents disagree, those documents are right.

Calculator outputs are checked against independently constructed amortization schedules built outside the site's own code, so that a bug in the code cannot validate itself. Worked examples published on this site are computed by hand and must reconcile with the tool before publication. Rules and thresholds cited anywhere on this site are traced to the statute, regulation, or agency handbook that creates them. The full process is in the editorial policy.

If you find a discrepancy, please report it — via the contact form or at pacificledgerstudio@gmail.com. Reader reports are the main way errors get caught, and what happens next is set out in the corrections policy.