Comparison
Mortgage Principal and Interest Crossover Across Rates: How Far Before the End It Happens, and When It Happens at All
How far before the end of a fixed-rate mortgage does the principal portion of each payment overtake the interest portion, and how does the interest rate move that point?
The short answer
The crossover sits a fixed distance from the end of the loan, and the interest rate alone sets that distance. At 6.0% it is the payment with138 payments left to run, counting itself. That is true of a thirty-year loan and of a fifteen-year loan at the same rate, and it does not depend on how much was borrowed.
What the term decides is whether the crossing happens at all. It needs at least 139 payments at 6.0%, and below that the first payment is already principal-majority and nothing is ever crossed. These are outputs of a calculation model applied to stated assumptions, not observations of any market.
- Who it applies to
- Fixed-rate, fully amortising, level-payment monthly loans. The rates below are inputs to an identity. None of them is a current, typical, offered or forecast rate, and no lender or product is named anywhere on this page.
- What this does not tell you
- It does not say what a mortgage costs, what any rate is, or whether any borrowing arrangement is sensible. It locates one crossing point inside a repayment schedule and nothing else.
Model Mortgage Mechanics v1.0. No market data, no rate level and no dated observation, so there is nothing here that goes out of date.
What is being compared
One question is asked of every rate in the same way, so the rates can be read against each other rather than one at a time. Nothing varies between rows except the interest rate.
| Loans modelled | Fixed rate, fully amortising, level payment, one payment per month, no overpayment and no fees. Nothing else. |
|---|---|
| Rates compared | 1.5% · 2.0% · 3.0% · 4.0% · 6.0% · 8.0% · 12.0%, as nominal annual rates convertible monthly |
| What the rate means | The note rate, converted to a monthly rate by dividing by twelve. Not an effective annual rate, not an APR and not a periodic rate. |
| Amount borrowed | Absent by proof rather than by choice. The condition the crossover turns on has no principal in it, so every figure below holds at every loan size. |
| Length of the loan | Absent from the offset for the same reason. Term decides whether a crossing happens at all, and converts the offset into a payment number. It does not move the offset. |
| Crossover measured | The payment split: the principal portion of one payment against the interest portion of that same payment. The cumulative comparison is a different question and has its own section below. |
| Units | Whole payments throughout. No currency, monthly amount, total interest or property value is modelled or shown. |
The rates are model inputs: values spaced so the structure is legible across the table, not rates anybody has offered, forecasts, or claims about what borrowing costs. UBWHY publishes no mortgage rate, no lender and no product anywhere, and this table is not one. No row here is described or implied to be current, typical, attractive or achievable.
The relationship, written once
Interest is charged on what is still owed, so the interest portion of a payment depends on how much of the loan is left. Work backwards from the last payment instead of forwards from the first and the arithmetic collapses to one line. Writing m for the number of payments still outstanding including the one being looked at, and i for the monthly interest rate, the principal portion exceeds the interest portion exactly when:
(1 + i)m < 2
m counts payments remaining, so it is a distance from the end of the loan rather than a position in it. i is the nominal annual rate divided by twelve, which is the convention a note rate is quoted under. Two things are missing from that line and their absence is the whole finding: the amount borrowed is not in it, and neither is the length of the loan.
The amount cancels because the monthly payment appears on both sides of the comparison and divides out. The term never enters because the condition is written in payments remaining. So the largest m that satisfies it is a property of the rate, and everything below is that one number read in different units. A reader who prefers the plain-language version can skip the line above: the crossing happens once the remaining term is short enough that the loan would not quite double at its own monthly rate over what is left.
How far before the end the crossover happens
Read a row and the answer is a distance from maturity, not a payment number. The distance counts the crossover payment itself, so it is what is left to run once that payment has been made, plus that payment. The last column is the same quantity again: the shortest loan the crossing fits inside, which is one payment longer than the distance.
| Nominal annual rate | Monthly rate | Payments remaining at the crossover | The same distance as time | Shortest term that crosses at all |
|---|---|---|---|---|
| 1.5% | 0.1250% | 554 payments | 46 years 2 months | 46 years 3 months |
| 2.0% | 0.1667% | 416 payments | 34 years 8 months | 34 years 9 months |
| 3.0% | 0.2500% | 277 payments | 23 years 1 month | 23 years 2 months |
| 4.0% | 0.3333% | 208 payments | 17 years 4 months | 17 years 5 months |
| 6.0% | 0.5000% | 138 payments | 11 years 6 months | 11 years 7 months |
| 8.0% | 0.6667% | 104 payments | 8 years 8 months | 8 years 9 months |
| 12.0% | 1.0000% | 69 payments | 5 years 9 months | 5 years 10 months |
The ladder doubles rather than stepping by one point, and that is the structure rather than a presentation habit. The distance is very nearly inversely proportional to the rate, so equal steps in the rate would compress almost the whole relationship into the low end: between 1.5% and 2.0% the distance moves by 138 payments, and between the last two rows by 35 payments. Each rate below is a third or a half larger than the one above it, alternately, so every second step doubles the rate and every rate has its own double inside the table.
Doubling the rate very nearly halves the distance
The ladder is built so that every rate has its own double inside it. Reading the pairs off the table gives the relationship directly, without any algebra:
| Rate | Double the rate | Distance at the lower rate | Distance at the higher rate | Ratio |
|---|---|---|---|---|
| 1.5% | 3.0% | 554 | 277 | 2.000 |
| 2.0% | 4.0% | 416 | 208 | 2.000 |
| 3.0% | 6.0% | 277 | 138 | 2.007 |
| 4.0% | 8.0% | 208 | 104 | 2.000 |
| 6.0% | 12.0% | 138 | 69 | 2.000 |
4 of the 5 pairs land on exactly two. The 3.0% pair gives 2.007 instead, and it is named rather than rounded away: the underlying quantity is not exactly halved, it is rounded to a whole payment at each rate, so a pair can miss by one. The relationship is close to exact rather than exact, and it is close for a reason that survives every rate: the distance is very nearly a fixed number divided by the monthly rate.
This is a property of the arithmetic, not a rule about borrowing. It does not say a higher rate is better, cheaper or worse. A higher rate brings the crossing closer to the end of the loan and costs more interest over the whole of it, and those two facts are not in tension: they are the same fact seen from two ends.
Two different questions share the word crossover
Published figures for "the crossover" disagree with each other, and some of the disagreement is not arithmetic at all. Two different comparisons are in circulation under one word, and they have different answers for the same loan.
- Payment split
- The principal portion of one payment exceeds the interest portion of that same payment. It happens in every loan in this model. This page is about this one, and every figure above is this one.
- Cumulative
- The total principal repaid so far exceeds the total interest paid so far. A different question, frequently a different answer, and on many loans it has no answer at all: it happens only if the total interest over the whole loan comes to less than the amount borrowed.
At 3.0% over 30 years the two land far apart. The payment split crosses at payment 84, and the cumulative comparison crosses at payment 161. Both are correct answers to their own question, and a source quoting one of them against the other's definition is not making an arithmetic mistake. It is answering a different question.
At 6.0% over 30 years the gap is wider still. The payment split crosses at payment 223, and the cumulative comparisonnever crosses at all: over the whole loan the interest comes to more than the amount borrowed, so the running total of interest is never overtaken.
The cumulative crossover is defined here and is not published as a reference of its own, because nothing follows from reaching or missing it. It changes no payment, no balance and no decision. It appears on this page for one reason: without it, a reader cannot tell which question a figure found elsewhere was answering.
One rate, two terms, one distance
The clearest way to see that the term does not move the offset is to hold the rate still and change the term. Both loans below are at 6.0%, and both resolve through the same model run.
- 30 years. The crossover is payment 223 of 360, which is 360 minus 138 plus one, and leaves 138 payments to run including itself.
- 15 years. The crossover is payment 43 of 180, which is 180 minus 138 plus one, and leaves 138 payments to run including itself.
Two payment numbers, one distance. Read forwards, one loan crosses in its nineteenth year and the other in its fourth, and the two look unrelated. Read backwards, both crossed with 138 payments left. The fifteen-year loan is not amortising differently. It is the last 11 years 6 months of the thirty-year one, and it starts closer to the end.
This is why a figure quoted without its rate cannot be checked, and why two published figures for two different terms can both be right and still look contradictory.
When the crossover does not happen at all
Below a certain term the crossing does not occur inside the loan. That is not a loan that crosses late, and it is not a loan that crosses at payment one. It is a loan that was never interest-majority, so there was no state to leave.
- Long enough — the term exceeds the rate's distance
- The loan starts interest-majority and leaves that state at the payment with 277 payments still to run, at a rate of 3.0%. Over 30 years that is payment 84.
- Principal-majority from the first payment
- At 3.0% the crossing needs a term of at least 23 years 2 months. A loan of 15 years is shorter than that, so more of its very first payment goes to principal than to interest and every payment after it does too. The model reports this as its own state rather than as a crossover at payment one, because nothing was crossed. This is the case that makes the common claim that early mortgage payments are almost all interest false as a general statement: it is true at some rates and terms and not at others.
- A rate of zero
- Every interest portion is exactly 0, so the whole of every payment is principal from the first one onward. The model takes an explicit branch here rather than approaching it as a limit, and the state it reports is the same principal-majority-from-the-start state above. No distance is published, because there is no crossing.
The reference table stops at 1.5% for the same structural reason and not for an editorial one. Below about 1.39% the crossing would sit further from maturity than the longest loan the model accepts, which is 50 years. The model states no distance there, so neither does this page.
Why published crossover figures disagree
Search results for this question return numbers that do not agree, and there are three separate reasons rather than one. Each is checkable against the table above.
- Different rates, unstated. A crossover figure is meaningless without the rate it was computed at, and the rate is frequently omitted. Bankrate publishes the crossing as year 18 or 19 on a thirty-year loan and year three or four on a fifteen-year one, and names no rate for either. Both are consistent with about 6.0%, where this model gives payment 223 and payment 43. They are the same distance from the end, and the page holding both does not say so.
- Different definitions. Some sources define the crossover as the cumulative comparison rather than the payment split. Those figures are answers to the question in the previous section and cannot be compared with these ones.
- Ordinary disagreement. Two reputable sources give the crossing at 4.0% over 30 years as two different payments, one apart. This model puts the crossing 208 payments from the end, which on that term is payment 153. A single payment is a small disagreement and it is still the difference between a figure that reproduces and one that does not.
None of this is offered as a correction to anybody. Two of the sources cited below publish figures that reproduce exactly, and one of them states the independence from the amount borrowed more plainly than this page does. The point is narrower: a crossover figure travels badly without its rate, its term and its definition attached, and that is why all three are attached to every figure here.
A crossover date is not a decision
Nothing changes on either side of the crossover. The payment is the same, the rate is the same, and the balance falls on exactly the path it was already on. It is a description of a repayment schedule, not an event, a milestone worth waiting for or a reason to act.
A later crossover is not a worse loan and an earlier one is not a better one. A shorter term brings the crossing forward and costs less interest in total; a lower rate pushes it later in the loan and costs less interest in total as well. The crossing point moves for reasons that point in opposite directions, so it cannot be read as a score.
This model describes fixed-rate, fully amortising, level-payment monthly loans. It does not model variable rates, overpayments, lender rounding, fees, APR, taxes, insurance, refinancing or affordability, and the word mortgage covers many contracts that are none of these things. None of this is financial, legal or tax advice, and no lender, broker, product or rate is named, ranked or recommended anywhere on this page.
What this reference does not determine
The figures on this page are outputs of a UBWHY calculation model applied to the assumptions stated above. They are not market data, an observation, a probability or a forecast. The reference cannot determine:
- what any mortgage rate currently is, has been or will be, none of which is named anywhere here
- what any lender, broker or product offers, none of which is named, ranked or compared
- whether any rate above is available to anybody, or has ever been available
- what a mortgage costs per month, in any currency, at any size
- whether a shorter term, a longer term or a different rate is a better arrangement
- whether overpaying, remortgaging or refinancing would be worthwhile, all of which the model excludes by name
- anything about variable, tracker, discounted, interest-only or offset arrangements
- fees, arrangement charges, insurance, property taxes or anything else outside the principal and interest
- APR, which is a different quantity computed under a different convention
- whether any borrowing is affordable, appropriate or safe for any particular person
The model carries full precision and rounds nothing per payment, so a lender's schedule will differ from it by a few units of currency in the final payment. That divergence does not move any figure on this page: every one of them is a count of payments, and a rounding difference of a few units cannot move a crossing that turns on a comparison between two portions of the same payment.
Where these figures come from
Every number above is produced by Mortgage Mechanics v1.0, run at build time over the reference set. Nothing on this page is typed by hand and no second formula was written to produce it. The model carries no route of its own: no mortgage calculator was earned here, because every finding above is independent of the amount borrowed and therefore needs nothing from a reader.
Six published figures are additionally reproduced by the model's own verified test cases, each recalculated on every run by an independent verifier that steps every payment in sixty-digit arithmetic rather than evaluating the same closed forms. MA-1 and MA-2 are 6.0% over thirty and fifteen years and carry the invariance itself. MA-7 is the 4% case two sources disagree about. MA-8 is 3.0% over thirty years, where the two crossovers land at different payments. MA-10 is the loan that is never interest-majority, and MA-3 is the zero-rate branch. The remaining figures are pinned by exact regression tests against the same model, including the monotonicity of the ladder and the reconstruction of every published payment number from its rate's distance.
Sources
Secondary reporting
Reporting that relies on other sources. Used only where primary material is unavailable.
When will I begin paying more principal than interest?
Supports: That the payment at which principal first exceeds interest is already published for individual thirty-year cases, and that the amount borrowed does not move it. It gives approximate crossover payments of 84 at 3%, about 120 at 3.5% and about 154 at 4% on a thirty-year loan, and states that “the amount of the loan doesn’t come into play at all”.
Cited for what it publishes and for what it does not. Its figures are stated as approximations and its 3% case agrees exactly with the UBWHY model; its 3.5% and 4% cases differ from the model by four payments and by one. It counts forward from the start of the loan only, publishes no rate-to-crossover table and no formula, and does not distinguish the per-payment crossover from the cumulative one.
When Do Homeowners Pay More in Principal Than Interest?
Supports: That the per-payment crossover and its independence from the amount borrowed are both already published. It gives the tipping point as the 84th payment at 3%, the 153rd at 4% and the 195th at 5% on a thirty-year loan, and states that the loan amount “does not affect when payments toward principal outweigh payments towards interest”.
Cited for the three thirty-year points it publishes, all of which the UBWHY model reproduces exactly, and for its explicit statement of principal independence. Its 4% figure of 153 differs by one from the 154 published by HSH above for the same rate and term. It counts forward from the start of the loan, addresses only the per-payment crossover, and publishes no formula and no rate-to-crossover table.
Supports: That a dominant amortisation surface publishes the crossover for two different terms without naming a rate for either and without relating them. It states that on “a conventional 30-year fixed loan, the point where more of your monthly payment goes toward principal than interest typically doesn’t occur until year 18 or 19” and that “a 15-year mortgage, on the other hand, typically reaches its tipping point by year three or four”.
Cited as the clearest instance of two published figures that are the same fact. Both are consistent with a rate of about 6%, at which the UBWHY model puts the crossover at payment 223 of a thirty-year loan and payment 43 of a fifteen-year one, which are the same 138 payments from maturity. The page names no rate, counts forward from the start of the loan in both cases, and does not state the relationship between them.
Mortgage Principal Calculator — Principal vs Interest Per Payment
Supports: That published crossover figures for one identical scenario can disagree with each other. For a thirty-year loan at 7% it gives the crossover as month 242 in one place on the page and as month 253 in another, and it publishes no rate-to-crossover table.
Cited for the disagreement rather than against the page. The UBWHY model puts the per-payment crossover at payment 242 for a thirty-year loan at 7%, which is one of the two figures the page gives. It counts forward from the start of the loan and does not distinguish the per-payment crossover from the cumulative one.
30 Year Mortgage Principal and Interest Chart Explained
Supports: That current sources use the word “crossover” for the cumulative comparison as well as for the per-payment one, and that the two are conflated in live material. It defines the crossover point as “where cumulative principal paid finally exceeds interest” and places it in years 15 to 18 of a thirty-year loan without naming an interest rate.
Cited only to establish that the ambiguity is real and current, not to correct one page. The definition it gives is the cumulative crossover rather than the per-payment one, and under the UBWHY model a cumulative crossover in years 15 to 18 of a thirty-year loan requires a rate of roughly 3.1% to 3.4%. Above about 5.30% at that term the cumulative crossover does not occur at any payment. No figure from this source is reproduced as a UBWHY figure.
UBWHY's own work
Calculations and reconstructions produced by UBWHY, recorded so the method can be examined. Not independent evidence, and not verification of the records they are built from.
UBWHY Mortgage Mechanics calculation model
UBWHY calculation model specification — Mortgage Mechanics, calculation model version “Mortgage Mechanics v1.0”, locked 17 August 2026. Held in the UBWHY repository and not published as a document.
Supports: UBWHY’s own calculation model and every figure on the mortgage crossover reference: the payment-split condition that the principal portion of a payment exceeds its interest portion exactly when the remaining payment count m satisfies (1 + i)^m < 2, where i is the nominal annual rate divided by twelve; the resulting independence of that count from the amount borrowed and from the length of the loan; the shortest term at which a crossing occurs inside a loan at all; the separate cumulative crossover and the rate above which it never arrives; and the explicit zero-rate branch in which every interest portion is exactly zero.
UBWHY’s own working specification, not independent evidence, and filed as such. Its arithmetic is verified twice against the published test vectors MA-1 to MA-12: once by the production model that renders this site and once by an independent verifier that steps every payment in sixty-digit fixed-point arithmetic rather than evaluating the closed forms. It models fixed-rate, fully amortising, level-payment monthly loans only. It contains no lender, product, jurisdiction or market rate of any kind, states no current or typical rate, and retrieves nothing at build time or at run time.
Figures that UBWHY calculates, and the conclusions drawn from them, are UBWHY's own work and are labelled as such in the text. They are not claims made by any source above.