Your figures

Your arrangement

Four figures, all yours. Nothing is sent anywhere, nothing is stored, and no rate, charge or provider is looked up. This calculator does not work out what you can afford to draw, and there is nothing in it that could.

The balance you are drawing from. No currency is assumed and none is printed: doubling this figure and the monthly amount together leaves every answer on this page unchanged, so the unit you enter is the unit you read back.

Your figure, level, every month. It is an input and never an output: this page will not tell you what this number should be, and the arithmetic here contains nothing that could work it out.

An assumption you are stating, not a projection this page makes. It is applied evenly every month at the twelfth root, so it is the same rate in every month of every year — which is precisely what a real pot does not experience.

Everything charged as a percentage of what the pot holds — platform, fund and adviser charges together, if all three are percentages. A fixed monthly charge is a different shape and is not modelled here.

Result

Enter your four figures above and select Calculate. Nothing is sent anywhere: the calculation runs in this browser, and no value is stored, shared or placed in the address bar.

The fee as a share of everything you draw
Not yet calculated
When the pot runs out, with the fee
Not yet calculated
When it would run out with no fee at all
Not yet calculated
Everything the arrangement pays out
Not yet calculated
Everything the fee takes
Not yet calculated
What the same arrangement would pay out with no fee
Not yet calculated
Result
Not yet calculated

This is arithmetic on four numbers you enter, not a plan. It runs one steady return, one level withdrawal and one fee to their arithmetic conclusion; a real pot meets a different return every month, and the order those returns arrive in changes the answer in a way nothing on this page can see.

The month reported is not a prediction and not a recommendation. It is what your own assumptions produce if every one of them holds exactly. This page will not tell you what you can afford to draw, and there is nothing here that computes it.

How this is worked out

What is being compared

Two runs of the same arrangement, differing in one thing. Every figure this tool reports is the difference between them.

The comparison. Neither row is a recommendation.
PathWhat it isWhen it ends
Your arrangementThe pot, the withdrawal and the return you entered, with the fee charged every monthThe first month a full withdrawal cannot be paid
The same arrangement, no feeThe identical pot, withdrawal and return, with the fee set to zeroThe same month, computed the same way, on the path with nothing taken out

One month, in full

Writing B for the balance the month opens with, g for the assumed annual return, F for the annual fee and W for the withdrawal:

growth factor    m_g = (1 + g) ^ (1/12)
retention factor m_f = (1 − F) ^ (1/12)
closing balance  B'  = B × m_g × m_f − W

The twelfth root, not a twelfth. A rate divided by twelve is not the monthly equivalent of an annual one, and the difference compounds over a path that runs for decades.

The pot runs out in the first month where B × m_g × m_f is less thanW. That month pays whatever is there and the path stops: there is no negative balance and no borrowing, because neither is a thing a pot does.

Why the answer is a difference and not a date

A single depletion date is worth very little. It is dominated by the return you assumed, and you cannot know that return.The difference between two dates computed from the same assumption is worth a great deal more, because the assumption you could not defend appears on both sides and largely cancels.

It does not cancel entirely, and this page does not claim it does. A higher assumed return makes the fee cost more months, not fewer, because the fee is charged on a larger balance for longer. Trying two returns and comparing the two differences is a more useful thing to do with this calculator than trying to find the right one.

The share of income has no upper limit

The second figure this tool reports is the fee as a share of everything the arrangement pays out. It is not capped at 100%, and a figure above it is not an error. The fee is charged on the balance and the share divides it by the income, so an arrangement drawing a small income from a large pot can pay a fee worth several times everything it ever draws.

The model's own verifier refused a first draft of the invariant that claimed otherwise. The claim was false and was corrected rather than the check being weakened.

What you enter

The pot
An amount, in your own currency. Nothing here assumes or prints one
The withdrawal
A level monthly amount, in the same currency. Yours, and never solved for
The return
An effective annual rate you are assuming, before the fee
The fee
An effective annual percentage of the balance

What is assumed

  • The return is a single rate applied evenly every month, at its twelfth root rather than a twelfth of it. That is what makes the answer a date rather than a range of dates.
  • The withdrawal is level and never changes, is never indexed and never pauses.
  • A month runs in the order growth, fee, withdrawal. A fee taken after the withdrawal would be charged on a smaller balance and would report a smaller cost for the same arrangement.
  • The date reported is the first month a full withdrawal cannot be paid — the month the income stops arriving in full, not the month the balance reaches zero. Whatever is left in that month is paid, and the path stops.
  • The path is run for a hundred years. That bounds the loop rather than the answer: a longer bound never changes a date that was already found.
  • Where the withdrawal never takes more than the return adds, the pot is reported as never running out. That is a property of the arrangement, not of how far the path happened to be run.

What is not modelled

Each of these moves the answer, and none of them is in the arithmetic. The first is the largest and is the reason no date on this page should be treated as a plan.

  • the order returns arrive in — a bad decade at the start empties a pot that the same average return over the same years would not
  • inflation, and any indexation of the withdrawal to it
  • a withdrawal that changes, pauses or steps down
  • the State Pension, an annuity, or any other income arriving alongside
  • tax on the withdrawal, in any jurisdiction
  • a fixed platform charge, a transaction cost or an adviser fee charged separately
  • anything about whether the level of income entered is a sensible one

The mechanism a percentage charge uses to compound against a balance is the same one running in the other direction here. The explainer on how investment fees compound covers it in full, and needs no JavaScript at all.

Go deeper

  • The nearest published mechanism

    How Investment Fees Compound Into Lost Wealth

    Why a small annual investment fee can create a much larger long-term difference, why the second component of that difference is signed, and where the arithmetic stops.

    The same charge, running against a balance that is growing rather than one that is being emptied. It is the mechanism this calculator applies, taught without any arithmetic to enter.

    Read the explainer: How Investment Fees Compound Into Lost Wealth

Calculation model and corrections

Calculation model
Withdrawal Path v1.0
Last reviewed
The withdrawal
Yours, level, every month, and never solved for. This calculator states no sustainable rate and has nothing in it that could compute one
The month
Growth first, then the percentage fee, then the withdrawal. A fee taken after the withdrawal would be charged on a smaller balance and would report a smaller cost for the same arrangement
Rates
Effective annual. The monthly factors are twelfth roots, not twelfths — the site converts a rate in exactly one place
The date reported
The first month a full withdrawal cannot be paid, which is the month the income stops arriving in full — not the month the balance reaches zero
The comparison
The identical arrangement with the fee set to zero. Same pot, same withdrawal, same return
The share of income
The fee divided by everything drawn. It has no ceiling, because the fee is charged on the balance and the share divides it by the income
The bound
A hundred years, and it bounds the loop rather than the answer. A longer bound never changes an answer that was already produced
Amounts
In whatever unit you enter the pot in. No currency is assumed or printed
Rounding
Display only; intermediate values remain unrounded

Correction history

  • Before publication, the model’s own verifier refused a first draft of its invariant claiming the fee could never exceed the income drawn. The claim was false and was corrected rather than the check weakened: the fee is charged on the balance and the share divides it by the income, so an arrangement drawing a small income from a large pot can pay a fee worth many times everything it ever draws. The figure this page reports is unbounded above and exactly zero at a zero fee.