Annuity calculator — methodology

Step one: the tax-free cash comes out before the annuity is bought

Normally 25% of a defined contribution pot can be taken free of income tax. That money leaves the pot, so what buys the annuity is what is left — not the whole pot with the cash subtracted from the income afterwards, which would quote an income on money already spent.

lump sum        = pot × tax-free rate
purchase price  = pot − lump sum

The rate is read from the rules file. The cap on it is not. See the limits section at the bottom.

Step two: the rate you were quoted, applied to that

An annuity rate is income per year for every £100 of purchase price, expressed as a percentage. The arithmetic is one multiplication, and it is the whole of what the rate does:

income a year   = purchase price × annuity rate
payment         = round(income a year ÷ payments a year)
income received = payment × payments a year

The third line is not pedantry. A whole number of pence per payment rarely multiplies back to the annual figure exactly, and the page taxes what is received rather than what the multiplication implied. It is also what makes the drawdown comparison exact: the pot on that side is charged the identical payment, so the two sides are the same cash flow rather than two cash flows that nearly agree.

An escalating income rises at each year boundary, from the base payment rather than from last year’s already-rounded one — payment × (1 + escalation)^year — which is the convention projection-core applies to a drawdown withdrawal, copied deliberately so the two sides cannot drift apart over a long term.

Step three: the tax, which is where the other income matters

Annuity income bought with pension savings is taxed as earned income in the year it is received. It is not a separate charge with its own rates: it goes on top of everything else taxable you receive and is charged at whatever rates that income has already reached.

taxable income = other income + annuity income received
income tax     = computeTaxPosition(taxable income, region, tax year)
tax caused by
the annuity    = income tax with it − income tax without it

The last line is a measurement rather than a rate applied to the income, and it has to be: an annuity income frequently spans two bands, and once other income is counted it can meet a rate that appears nowhere in a rates table. A calculator that asks “are you a basic or higher rate taxpayer?” and applies one rate to the whole income cannot be right for anyone whose income crosses a threshold.

Above £100,000 of total income the personal allowance is withdrawn at £1 for every £2 of income, so a pound of income there is taxed at its band rate and exposes another £0.50 the allowance had been covering — a marginal rate of 60.00% at the England, Wales and Northern Ireland higher rate, and more in Scotland. The page reports the rate on your next pound rather than describing it, and the distance to the next band is converted from the engine’s taxable income measure into the gross income figure you could act on. Those two are not the same number and printing the raw one under “how much more income” is a real defect this site has shipped before.

No National Insurance is charged on a pension income, at any age, so none is shown.

What taking tax-free cash actually costs, after tax

Every annuity purchase makes this trade and almost no calculator shows it. Cash taken as the tax-free lump sum is free of income tax for good. The extra income you would have bought by not taking it is taxable every year, at your marginal rate. So the comparison is not the cash against the extra gross income; it is the cash against the extra income after tax:

cash given up   = lump sum at the higher percentage − lump sum at the lower
income gained   = (purchase price difference) × annuity rate
what it is
actually worth  = income gained − tax on income gained, every year

The page computes that at nought, half and the whole of the statutory tax-free share, plus whatever you chose, taxing each one properly against your other income. The percentages are derived from the rules file rather than written down, so a tax year that moved the tax-free share cannot leave the panel pointing at a percentage that no longer exists. Which side of the trade suits you is not a question this page answers.

The same purchase price, drawn down instead

Two different questions, computed two different ways:

• Would a drawdown pay the annuity’s income? The pot is charged the identical payment, escalating identically, through a period-by-period schedule: apply the period’s growth, deduct the platform charge, take the withdrawal last. The balance floors at zero, a request larger than the pot is truncated to what is there, and once a payment cannot be made in full the income stops for good. The page reports the year of that first short payment, which is earlier than the year the balance reaches zero and is the answer that matters.
• What would a drawdown pay instead? Solved by bisection on the withdrawal: the largest per-period amount for which every payment is made in full, right through to the final period. One penny more and it is not. Divided by the purchase price, that is a percentage directly comparable with the rate you were quoted.

drawdown equivalent rate = sustainable income a year ÷ purchase price

Those two percentages are not the same kind of number, and the page says so wherever it prints them. The annuity rate buys an income for as long as you live. The drawdown equivalent runs out at the end of a term you typed in, and it moves every time the growth assumption moves. There is no life expectancy anywhere in this site and there is not going to be one, so the page puts the two figures side by side and declines to pick.

The tax comparison is the part readers most often expect to be interesting and it is not: both incomes are taxed identically, so at the same gross income the tax is the same tax. Saying so is worth more than a table, because the belief that one is taxed more favourably than the other is common and wrong.

Rates and allowances

Thresholds are taxable income, after allowances. The Scottish bands apply to an annuity bought with pension savings because that income is earned income and income tax on it is devolved. No annuity rate appears in this table or anywhere else in the rules files, because none is a statutory figure.

Sources

• gov.uk — Income tax rates and allowances: current and pastAnnuity income bought with pension savings is taxed as earned income, so the ordinary bands, the personal allowance and its taper are what apply to it.
• gov.uk — Tax when you get a pension
• gov.uk — Pension schemes rates and allowancesThe lump sum allowance is published here and is deliberately not modelled — see the limits section below.
• gov.scot — Scottish income tax rates and bandsIncome tax on a pension income is devolved, so a Scottish annuitant meets a different set of bands.

The verification, and the parts of this page it covers

That stamp covers the tax calculation only. It is a check on the published rates, thresholds and allowances in the rules files. It does not reach the drawdown comparison — there is no published figure in a growth rate for anyone to check — and it says nothing at all about the annuity rate, which you supplied and which no part of this site verifies. Three claims, three scopes, kept apart on purpose.

The bounds on the input fields, and why they are not all the same kind of bound

• The annuity rate is bounded 0% to 100%, and that is not an engine limit. Both engines accept any non-negative rate here, so nothing in that range can throw. The ceiling is a statement about the word: at 100% the “annuity” returns the entire purchase price in the first year, which is a refund rather than an income for life. The floor is zero because zero is what an empty box means — “I have not told you a rate” — and an income of nothing is the right arithmetic for that.
• The growth assumption is floored at -99%, not −100%, and this one is the engine’s domain. The projection engine rejects an annual rate of exactly −1 — a total loss is not a growth assumption — and the field’s clamp is inclusive, so a floor of −100 would be an unhandled error reachable by typing a minus sign. The income escalation is floored at -99% for the same validator.
• The drawdown charge is capped at 5% a year. The solver that finds the largest income lasting the term bisects, and bisection is only trustworthy while its objective is monotone — which fails when a periodic charge exceeds the balance it is charged on. That needs more than 1,200% a year at monthly periods, so the cap discharges the precondition rather than a guard doing it after the fact.
• The tax-free lump sum is capped at the rate, 25%, which is the only part of the tax-free lump sum the tax engine models.
• An empty field means zero, not the bottom of the range. Clearing the growth box asserts no growth, not the -99% at the floor.

Limits that change the answer, stated here rather than buried

• Every determinant of an annuity rate. Age, health, smoking status, postcode, guarantee period, survivor’s pension, value protection, payment in advance or in arrears, and whether the income escalates all change what an insurer offers. None is priced here, because pricing them needs mortality data and an insurer’s own loading. Enter the rate quoted for the shape you actually want — a quote for a level single-life annuity is not a quote for an escalating joint-life one.
• The lump sum allowance is not applied. The tax-free 25.00% is a verified figure; the cash cap on it is not in the tax engine’s schema at all. On a pot large enough for 25% to exceed the allowance, this page shows more tax-free cash than could actually be taken, and therefore too little tax.
• Emergency tax on a first payment is not modelled. A provider commonly operates a month-1 code on a first payment, taxing it as though it were the first of twelve identical ones. Far too much comes off and it is reclaimed afterwards. This page shows the tax-year position, which is where you end up, not what comes off the payment.
• One tax year’s tax. The tax figures describe the first year. The drawdown comparison runs for the whole term but does not re-tax each year’s income against a future year’s bands, because nobody knows what those bands will be — the calculator offers the tax years it has rules files for and no others.
• Purchased life annuities are taxed differently and are not this. An annuity bought with money that is not pension savings has part of each payment treated as a return of capital. This page models an annuity bought with a defined contribution pension pot.
• Nothing about you. No life expectancy, no health, no partner, no other savings, no care costs. This site publishes information, not advice: it recommends no product, no provider and no course of action, it does not tell you whether to annuitise, and no figure on it is a personal recommendation.