Comparison
Rolled-Up Debt and Remaining Equity: How Long Before the Balance Doubles, and What Is Left of the House
When interest is added to a balance that is never repaid, how many years does it take to double — and how much of the property is still the holder’s when it has?
The short answer
The doubling time depends on the rate and on nothing else — not on the amount, not on the property, not on the size of the release. At 6% a rolled-up balance doubles in 11.9 years. A balance that started at 30% of the property leaves 10.00% of it once it has tripled, and nothing at all after 20.7 years.
The figure an offer leads with is the sum released, and the sum is the part of it that carries no information about the cost. Two households borrowing very different amounts against properties in the same proportion are in the identical position, at every horizon and at every rate. What decides the outcome is the share, the rate and how long the arrangement runs — and the last of those is not chosen by anyone.
- Who it applies to
- Any borrowing where interest is added to the balance and nothing is repaid until the property is sold — a roll-up lifetime mortgage is the ordinary case. It compares rates, horizons and shares, not lenders, products or contracts.
- What this does not tell you
- It establishes how fast a balance nobody repays grows and what share of the property that leaves, and nothing else. It does not establish what any lender charges, what a contract does once the balance reaches the value, or what a property will be worth.
An exact identity rather than a projection: one growth factor and two logarithms, so no calculation-model version, no assumed return and no market figure enters the answer, and nothing here goes out of date.
What is being compared
Four ladders, held against each other in pairs. Nothing varies except the quantity a table's axes name, and no amount of money appears anywhere on this page.
| Roll-up rates compared | 4% · 5% · 6% · 7% · 8% |
|---|---|
| Horizons compared | 5y · 10y · 15y · 20y · 25y |
| Opening shares compared | 15% · 20% · 25% · 30% · 40% · 50% |
| Growth factors compared | ×1.50 · ×2.00 · ×2.50 · ×3.00 · ×4.00 |
| Repayments | None. That is what a roll-up is, and it is the whole mechanism |
| Amounts | None. No published quantity contains the amount borrowed |
| Property value | Held constant. An assumption, stated as one, and not a forecast |
| Compounding | Annual, on an effective annual rate. A rate quoted as an AER already is one |
| Fees added to the balance | Not modelled. Where they exist they raise the opening share |
| Further drawdowns | Not modelled. Each one starts its own factor from its own date |
Every rung on every ladder is a stated level entered into the identity, chosen so the shape can be read. None of them is a survey of what is charged, released or typical, no lender or product is named, and nothing here reports a market condition.
Where the growth comes from
A roll-up takes no payment. Interest is added to the balance, and next year's interest is charged on that larger balance, so the balance follows a single factor:
balance after n years = balance at the outset × (1 + r)^n
Divide both sides by the balance at the outset and the amount borrowed disappears. What remains is (1 + r)^n — a pure multiple — and it is the whole of the mechanism.Every quantity on this page is that multiple, or a rearrangement of it, and not one of them contains a sum of money. The doubling time is the year in which the multiple reaches two. What is left of the property is one minus the opening share times the multiple. The year there is nothing left is the year the multiple reaches the reciprocal of the opening share.
The property is held at a constant value throughout, and that is an assumption rather than a prediction. Adjusting it needs one division and no new table: if the property ends the period worth p times what it started at, every equity figure below becomes1 − a × m ÷ p. A property that gains value slows the erosion; one that loses value brings every horizon here forward. This page states neither, because a property-price assumption is a forecast, and publishing a ladder of them would be publishing a forecast whichever rungs were chosen.
How long a rolled-up balance takes to double
One column, and it takes no horizon, no amount and no property value. That is the point of putting it in its own table before the grids: the doubling time is a property of the rate alone.
| Roll-up rate | Years to double |
|---|---|
| 4% | 17.7 years |
| 5% | 14.2 years |
| 6% | 11.9 years |
| 7% | 10.2 years |
| 8% | 9.0 years |
The gap between the ends of that ladder is most of a decade, and it is the reason a rate comparison on this kind of borrowing is not the small print. Nothing else about the arrangement moves the doubling time at all.
What the balance becomes, by rate and horizon
The same factor, read at five horizons. Each cell is what the balance has become as a multiple of itself — so a cell of ×2.00 is the doubling above, arrived at from the other direction.
| Roll-up rate | 5 years | 10 years | 15 years | 20 years | 25 years |
|---|---|---|---|---|---|
| 4% | ×1.22 | ×1.48 | ×1.80 | ×2.19 | ×2.67 |
| 5% | ×1.28 | ×1.63 | ×2.08 | ×2.65 | ×3.39 |
| 6% | ×1.34 | ×1.79 | ×2.40 | ×3.21 | ×4.29 |
| 7% | ×1.40 | ×1.97 | ×2.76 | ×3.87 | ×5.43 |
| 8% | ×1.47 | ×2.16 | ×3.17 | ×4.66 | ×6.85 |
A lifetime mortgage has no term. It ends on a death or a move into care, so the horizon is not a choice anybody makes and the row is read across rather than at a point somebody selected. That is the fact this table exists to make unavoidable: the arrangement is entered at one end of the row and left at an unknown one.
What is left of the property
The rate and the horizon enter this answer only through the multiple, so the grid is indexed by the multiple rather than by both of them. Find the factor in the table above, then read down to the share the balance started at.
| Share borrowed at the outset | Balance ×1.50 | Balance ×2.00 | Balance ×2.50 | Balance ×3.00 | Balance ×4.00 |
|---|---|---|---|---|---|
| 15% | 77.50% | 70.00% | 62.50% | 55.00% | 40.00% |
| 20% | 70.00% | 60.00% | 50.00% | 40.00% | 20.00% |
| 25% | 62.50% | 50.00% | 37.50% | 25.00% | Nothing left |
| 30% | 55.00% | 40.00% | 25.00% | 10.00% | Nothing left |
| 40% | 40.00% | 20.00% | Nothing left | Nothing left | Nothing left |
| 50% | 25.00% | Nothing left | Nothing left | Nothing left | Nothing left |
An exact figure is one multiplication rather than an interpolation between columns: the share left is 1 − a × m, for the opening share a and the multiplem the table above gives. The ladder is there to show the shape, not to be read as the only cases that exist.
Nothing left is printed as a state rather than as a negative percentage, and the difference is not presentational. Past that point the balance exceeds the property, and what a holder or an estate then owes is a question about a contract — some carry a guarantee that the debt can never exceed the sale proceeds, and whether one applies is wording rather than arithmetic. A negative figure here would answer a contract question with arithmetic that had left its own domain.
The year there is nothing left
The same crossing, stated as a date rather than as a share. This is the second half of the question the page exists for, and it takes only the opening share and the rate.
| Share borrowed at the outset | 4% | 5% | 6% | 7% | 8% |
|---|---|---|---|---|---|
| 15% | 48.4 years | 38.9 years | 32.6 years | 28.0 years | 24.7 years |
| 20% | 41.0 years | 33.0 years | 27.6 years | 23.8 years | 20.9 years |
| 25% | 35.3 years | 28.4 years | 23.8 years | 20.5 years | 18.0 years |
| 30% | 30.7 years | 24.7 years | 20.7 years | 17.8 years | 15.6 years |
| 40% | 23.4 years | 18.8 years | 15.7 years | 13.5 years | 11.9 years |
| 50% | 17.7 years | 14.2 years | 11.9 years | 10.2 years | 9.0 years |
The last row is the doubling table again, and a reader can check it: a balance that started at 50% of the property reaches the whole of it exactly when it has doubled, so at 6% it runs out after 11.9 years — the same figure the first table gives. The doubling time is not a separate fact about compounding. It is this table at one particular rung, and it is the rung a reader is least likely to be at.
Read the top-left corner against the bottom-right one. Nothing in either cell is a forecast: both are the same arithmetic, and the distance between them is what the two choices actually decide.
A growth factor is not a contract
Everything above is arithmetic, and arithmetic is the smaller half of this question.This page cannot tell anyone what their contract does, and it does not claim that every arrangement behaves alike. Rates are fixed for life on some and not on others. Fees may be added to the balance at the outset, which raises the opening share before anything compounds. Voluntary partial repayments are permitted on some contracts and are what break the factor. Which of those applies is in the wording, and the wording is not arithmetic.
The figures are also conditional on a horizon nobody selects. A lifetime mortgage runs until a death or a move into care, so the reader entering one does not choose which column of the tables above they will end up in — which is the respect in which this differs from every borrowing decision with a term.
Two households with the same opening share can still be in different positions, depending on:
- the rate itself, which is fixed for life on some contracts and not on others
- fees added to the balance at the outset, which raise the opening share before anything compounds
- further drawdowns, each of which starts its own growth factor from its own date
- voluntary partial repayments, where they are permitted and where they are affordable
- what the property does in value, in either direction
- how long the arrangement actually runs, which nobody chooses
- what the alternative was, and what it would have cost
No level of release is presented here as sensible or reckless, and nothing on this page argues against releasing equity. Money now is worth something, and for some households it is worth a great deal; what the tables above price is what it costs, which is a different question from whether it is worth paying.
What this comparison does not determine
The figures on this page are exact arithmetic on stated rates and stated shares. They are not quoted offers, contract terms, market rates or a forecast of anything. The comparison cannot determine:
- what any lender charges, offers, or would lend against any property
- whether a contract carries a no-negative-equity guarantee, and on what terms
- what an early-repayment charge would cost, or whether one applies
- whether voluntary partial repayments are permitted, and what they do to the balance
- what fees are added to the balance at the outset, or when
- how a drawdown facility releases further amounts, or what each one then costs
- what happens on a move into care, on a death, or on a sale
- what a property is worth, what it will be worth, or how its value should be measured
- how long anyone will live, which is the horizon this arrangement actually runs for
- whether releasing equity is suitable, affordable or advisable for anyone
It also holds the balance still except for interest. A contract that permits and receives voluntary repayments does not follow this factor at all, and one that releases further amounts follows several factors starting on several dates. Both are real and neither is modelled here, because the identity is a statement about one balance compounding undisturbed.
None of this is financial, legal or tax advice, and no product, provider, lender or contract is recommended, ranked or named anywhere on this page.
Where these figures come from
Every number above is produced at build time from balance after n years = balance at the outset × (1 + r)^n, applied to the four ladders in the comparison set. Nothing on this page is typed by hand, and nothing is calculated in the browser.
There is no calculation-model version behind them, and that absence is the point. A growth factor and two logarithms are closed forms rather than a projection, so they inherit no horizon, no assumed return and no rate that anybody has to keep current. The regression suite holds every published figure against a second, independently written implementation, and pins the identity between the doubling time and the exhaustion horizon exactly rather than within a tolerance — two implementations that agree are evidence, one checked against itself is not.
The build refuses a rate at or below zero, an opening share at or above the whole property, and a growth factor below one, rather than reporting a figure for any of them. None is a case the identity has content at, and printing a boundary that is not a quantity would be worse than printing none.