# Methodology

> The exact arithmetic behind every SavingsLast calculator: the monthly loop, the tax gross-up, the solver, and an honest list of what the model ignores.

Source: https://savingslast.com/methodology/
Markdown: https://savingslast.com/methodology.md
Site: SavingsLast, free retirement drawdown calculators. Educational estimates, not advice.

Most retirement calculators won't tell you what they are doing. This page will, in enough detail that you could rebuild ours in a spreadsheet and get the same answer to the dollar.

## The simulation

Every calculator on this site runs the same loop, one month at a time, inside your browser. Nothing you type is sent to us or to anyone else.

Each month, in this order:

1. The balance earns one month of growth.
2. The withdrawal comes out.
3. Next month's withdrawal is increased a little for inflation.

The annual return you enter is converted to a monthly rate with (1 + r)1/12 − 1, not by dividing by twelve. On a 5% return that is 0.4074% a month rather than 0.4167%. The gap looks trivial and it is, but over 360 months it compounds into real money, and getting it right costs nothing. Inflation is converted the same way, so a 2.5% figure raises your withdrawal by exactly 2.5% over twelve months rather than 2.53%.

## One month, worked through

Take $500,000 at 5% growth, withdrawing $3,000 a month, with 2.5% inflation and no tax.

- Month one: $500,000 grows by 0.4074% to **$502,037.06**.
- The $3,000 withdrawal leaves **$499,037.06**.
- Month two's withdrawal rises to **$3,006.18**, and the loop repeats.

Run that forward and the money lasts **204 months — exactly 17.0 years**, with $758,304 withdrawn along the way. That is the number the calculator on the homepage shows, because it is running this same code.

## How tax is handled

The tax field assumes you want to *keep* the amount you typed. So the calculator grosses the withdrawal up: it removes withdrawal ÷ (1 − tax) from the balance. Asking for $3,000 a month at a 22% rate actually pulls **$3,846.15** out, leaving you the $3,000 you asked for.

This is a flat rate applied to the whole withdrawal. It is right for a traditional 401(k) or IRA, where every dollar out is ordinary income. It is wrong, and deliberately conservative, for a taxable brokerage account, where you are only taxed on the gain — for those, entering roughly half your capital gains rate gets closer. For a Roth, enter zero.

## The "how much can I withdraw" figures

The three boxes under each result are solved rather than estimated. We search for the largest starting withdrawal that still survives 20, 25 or 30 years under the same return and inflation you entered, using 40 rounds of bisection between $0 and your full balance. That converges to well under a cent. On $500,000 at 5% and 2.5%, the 30-year answer is $1,961 a month.

We solve it rather than applying the 4% rule because the 4% rule is a finding about one country's market history, not a formula. Your numbers deserve your numbers.

## Where the simulation stops

If the balance survives 1,200 months — a hundred years — we stop and report "indefinitely". At that point growth is outrunning your inflation-adjusted withdrawals and the exact year is meaningless.

## What we won't let you type

Returns and inflation accept −20% to 100%, and tax accepts 0% to 99%. Anything outside that reverts when you leave the field.

The limits exist because unbounded inputs produce confident nonsense. A 2000% return will happily report that your money lasts forever, which is true of the arithmetic and useless to you. We set the range wider than most — CalcXML allows −12% to 12%, Dinkytown 0% to 20% — because testing a genuinely bad decade at −15% is a reasonable thing to want, and refusing it would be patronising. Above 100% you are no longer planning, you are typing.

## What this model does not do

This is the section worth reading twice. Every calculator makes these compromises; most don't list them.

- **It assumes the same return every year.** This is the big one. Real markets are lumpy, and two retirees with identical average returns can end up in completely different places depending on whether the bad years land early or late. Withdrawing from a portfolio that just fell 30% locks in the loss permanently. A steady-return model cannot see that risk, and it is optimistic because of it. Treat the result as a baseline, then assume you need a margin on top.
- **It ignores fees.** A 1% advisory fee is simply a 1% lower return here, so subtract it from the figure you enter. Over thirty years that is not a rounding error.
- **The tax field is a single flat rate.** No brackets, no standard deduction, no state tax, no capital gains treatment, and no modelling of how withdrawals push more of your Social Security into taxable income — the "tax torpedo", which can make a 22% bracket behave like 40%.
- **The general calculators do not model required minimum distributions.** The account-specific ones now do — see below. On this page, and on the amount and age pages, no RMD is applied, so a plan that quietly underspends a traditional account will look better here than it would in reality.
- **It has no view on long-term care.** A meaningful minority of retirees face costs of $60,000 to $120,000 a year. That is not absorbable from most portfolios and needs insuring or ring-fencing separately.
- **It assumes you keep withdrawing on schedule.** Real retirees adjust. Trimming spending roughly 10% after a bad year historically adds years of portfolio life, and this model gives you no credit for that flexibility.
- **Amount-page tables assume 2.5% inflation and no tax**, so they are comparable across pages. The calculator on the same page is the one to trust for your own situation.

## The Social Security calculators

The claiming pages use the Social Security Administration's actual formulas rather than an approximation. Claiming before full retirement age reduces the benefit by five-ninths of 1% per month for the first 36 months, then five-twelfths of 1% for every month beyond. Delaying past full retirement age adds two-thirds of 1% a month — 8% a year — and stops dead at 70.

With a full retirement age of 67, that works out to **70% of your benefit at 62 and 124% at 70**. Break-even ages are found by accumulating both streams month by month with your cost-of-living assumption applied, and optionally compounding the payments you would have invested.

## Figures we quote across the site

The average retired-worker benefit we use is about $1,976 a month, from the Social Security Administration. The 4% rule comes from William Bengen's 1994 study in the *Journal of Financial Planning* and the 1998 Trinity Study; both examined U.S. market history and asked what withdrawal rate never failed over 30 years, which is a different question from what rate is optimal. IRA and 401(k) distribution rules follow IRS Publication 590-B. State tax treatment is reviewed annually and each state page carries its own review date and a link to the relevant agency.

Long-run averages we lean on: U.S. inflation has run about 2.5% over thirty years, and a 60/40 portfolio has historically returned roughly 6–8% nominal. Neither is a promise about the next thirty years.

## Rules the account calculators apply

The 401(k), IRA, 403(b), 457(b), TSP, SEP, SIMPLE, Roth, HSA, inherited IRA, rule-of-55 and early-withdrawal pages apply the rules that actually govern those accounts. They used to describe them and compute a generic answer, which meant the 457(b) page explained that no penalty applies and then produced arithmetic identical to the 401(k) page, where it does. That is fixed.

- **The 10% early-withdrawal penalty** is added to the tax gross-up for every distribution taken before 59½, so reaching a given after-tax income costs more of the balance. It stops automatically the month you reach 59½ rather than at the end of that year.
- **It is not applied** on the 457(b) page (governmental plans carry no penalty after separation at any age), on the rule-of-55 page, or on the inherited IRA page — in each case because the exception is the subject of that calculator.
- **The rule of 55 is not offered on the IRA pages**, because it does not apply to IRAs.
- **The 72(t) page does not run this drawdown model at all.** It computes the payment under the three methods in IRS Notice 2022-6, from the life expectancy and mortality tables in force since 2022. Every build checks that engine against ten examples the IRS has published. Each result shows the table it read, the factor it found, the rate it used and the division it did.
- **The HSA page** applies a 20% penalty before 65 rather than 10%, and treats qualified medical withdrawals as tax-free.
- **Required minimum distributions** begin at 73 on every traditional account, using the IRS Uniform Lifetime Table in force since January 2022. Each year the calculator takes the larger of your chosen withdrawal and the required minimum, so a plan that underspends is corrected upward the way the IRS would correct it. You must enter an age for this to apply.
- **Roth IRAs get no RMD at all** and ignore the tax field, which is disabled on that page.

Two honest limits. The SIMPLE IRA penalty is 25%, not 10%, within the first two years of participation, and the calculator applies the 10% figure. And an RMD you do not spend can be reinvested in a taxable account — this model removes it from the balance, which is correct for "how long does this account last" and pessimistic for how long your total wealth lasts.

## Why another calculator gives you a different number

Two honest calculators can disagree by years on the same inputs, because "how long will it last" is not one calculation. It depends on choices each tool makes and mostly does not tell you about. We checked ours against the others on **$500,000, $3,000 a month, a 5% return and 2.5% inflation**, no tax:

| Calculator | Result | What it assumes |
| --- | --- | --- |
| **SavingsLast** | **17 years 0 months** | Monthly loop, growth then withdrawal, inflation compounded monthly |
| CalcXML | ~17 years | The same four levers, including tax |
| Dinkytown (KJE) | 16 years 11 months | Annual withdrawals with an annual inflation step-up |
| Bengen / Trinity convention | 17.00 years | Annual compounding, withdrawal taken at the start of the year |
| calculator.net | 23 years 3.5 months | No inflation field at all |

**The one that matters is inflation.** A calculator that ignores it will tell you your money lasts about six years longer, on these numbers, than one that does not. That is not a rounding difference — it is the difference between a plan that works and one that quietly fails in your late seventies. If a tool has no inflation box, its answer is the answer to a different question.

The rest is convention, and it is worth a month or two either way. We withdraw monthly rather than annually and let the money keep earning until it is taken, which lands us one to two months ahead of Dinkytown on the same inputs. Neither is more correct; ours matches how a retiree actually draws income, and it agrees with the classic Bengen and Trinity annual convention almost exactly.

Two other differences worth knowing about when you compare tools: whether the withdrawal is taken at the start or the end of each period, and whether a tax rate reduces your growth or grosses up your withdrawal. We do the latter, which is set out under "How tax is handled" above.

## Found a mistake?

Tell us and we will fix it. The calculations here are deterministic and testable, so a bug is a bug rather than a matter of opinion — the engine is checked on every deploy against known results, including the $500,000 example above. Write to [hello@savingslast.com](mailto:hello@savingslast.com).