What portfolio longevity means
Portfolio longevity is the number of years a balance survives a given withdrawal. It is the same equation as a loan amortisation, run backwards: instead of a lender's balance falling as you pay it down, your balance falls as you draw it down, and the interest works for you instead of against you. That is why the answer has a logarithm in it, and why it behaves so violently near the break-even point.
The result is not a prediction. It is a consequence of four assumptions, and the assumption that does most of the work is the relationship between your return and your inflation rate. Withdraw 5% of a portfolio earning 5% nominal with no inflation and the money lasts a very long time. Withdraw 5% of a portfolio earning 5% nominal while inflation runs at 3%, indexing your spending, and the real return is only 1.94% and the money runs out in under 25 years. The nominal numbers look identical; the outcomes are not.
Two behaviours are worth understanding before you read any answer. First, longevity is extremely non-linear near the sustainable threshold: at a 4% real return, withdrawing 4% of the portfolio lasts about 83 years, while withdrawing 5% lasts about 37. One extra percentage point of spending cuts the horizon by more than half. Second, below the threshold the answer is not a large number, it is infinity — growth covers the withdrawal and the balance never falls.
Where the formula comes from
Work in real terms and the inflation problem disappears. If your spending rises with prices at rate π while the portfolio earns r, then measured in constant dollars the balance earns the real rate i = (1 + r)/(1 + π) − 1 and the withdrawal is a level amount W. That substitution turns an awkward two-growth-rate problem into a plain annuity.
Now write the balance after one year. You withdraw at the start, so the year begins with P − W, and that grows by (1 + i). Repeat, and the balance after n years is P(1 + i)n minus the accumulated value of n withdrawals. Set that to zero and you get the condition that the portfolio is exactly an n-year annuity-due: P = W · [1 − (1 + i)−n]/i · (1 + i). Solving for n gives the logarithm on this page; solving for W gives the maximum sustainable withdrawal.
Look at what has to be true for the logarithm to exist. The argument is 1 − P·i / (W(1 + i)), and it stops being positive once W(1 + i) drops to P·i. That is the perpetuity threshold: a withdrawal of P·i/(1 + i) is exactly funded by the first year's growth, so the balance repeats forever. At a 5% return that threshold is 4.76% of the portfolio; at a 3% real return it is 2.91%.
When the real return is zero the formula reduces to n = P / W, which is worth remembering as a floor. A million dollars withdrawn at $40,000 a year lasts exactly 25 years if the portfolio merely keeps pace with inflation, and every year beyond that is paid for by real growth.
Worked example: $100,000 at $10,000 a year and a 5% return
You have $100,000, you take $10,000 at the start of each year, you hold that dollar amount level rather than indexing it, and the portfolio earns 5% a year. Because the withdrawal is level in nominal dollars, the rate to use is the nominal 5%.
- Check the threshold. P·i = $100,000 × 0.05 = $5,000, and W(1 + i) = $10,000 × 1.05 = $10,500. The withdrawal is larger, so the portfolio does deplete.
- Form the fraction. $5,000 ÷ $10,500 = 0.476190.
- Subtract from one. 1 − 0.476190 = 0.523810.
- Take the logarithms. ln(0.523810) = −0.646627 and ln(1.05) = 0.048790.
- Divide. 0.646627 ÷ 0.048790 = 13.25 years. Starting at 65, the money runs out partway through the year you turn 78.
Check it by hand. Year one: $100,000 − $10,000 = $90,000, grown by 5% to $94,500. Year two ends at $88,725; year five at $69,609; year ten at $30,821; year thirteen at $2,579. The fourteenth withdrawal of $10,000 cannot be paid in full, which is exactly what a fractional answer of 13.25 years means.
Now hold the return at 5% and index the withdrawal to 3% inflation. The real rate becomes (1.05 ÷ 1.03) − 1 = 1.9417%, the threshold falls to $100,000 × 0.019417/1.019417 = $1,905, and the same $10,000 withdrawal now lasts only 11.0 years. Inflation indexing is not a detail.
Years a portfolio lasts, by withdrawal rate and real return
| Withdrawal rate | 0% real | 1% real | 2% real | 3% real | 4% real |
|---|---|---|---|---|---|
| 3% | 33.3 | 40.2 | 53.5 | 119.6 | never |
| 4% | 25.0 | 28.6 | 34.0 | 44.1 | 83.1 |
| 5% | 20.0 | 22.2 | 25.1 | 29.6 | 37.4 |
| 6% | 16.7 | 18.1 | 20.0 | 22.5 | 26.1 |
| 7% | 14.3 | 15.3 | 16.6 | 18.2 | 20.3 |
| 8% | 12.5 | 13.3 | 14.2 | 15.3 | 16.7 |
| 10% | 10.0 | 10.5 | 11.0 | 11.6 | 12.4 |
"Never" means the withdrawal sits below the perpetuity threshold i/(1 + i), so growth covers it in full. The calculator above caps its answer at 100 years for readability.
How to read the answer
Compare the depletion age with a realistic longevity, not an average one. Life expectancy at 65 is an average, and a large share of 65-year-olds live well past it; for a couple the chance that at least one partner is alive at 90 is far higher than for either individually. A plan that depletes at 88 is not a plan that works nine times out of ten; it is a coin flip.
Then look at how far you sit from the threshold. If your withdrawal is close to the sustainable maximum, the answer is fragile: a percentage point of return or a percentage point of extra spending moves the depletion date by many years. If it is well below, the answer is robust and the exact assumptions matter much less. The row spacing in the table above shows this directly — the top-left corner changes slowly, the bottom rows barely move at all.
Treat the smooth-return assumption as the main limitation. This model applies the same return every year, but real sequences are lumpy, and a bad first five years hurts a portfolio in drawdown far more than the same five years later, because you sell more shares at low prices to fund the same spending. That is sequence-of-returns risk, and it is why the historically calibrated rules in the safe withdrawal rate calculator land below what a smooth-return model would allow. A defensible way to use this page is to run it at your central assumption and again with the return reduced by two points, and to plan against the worse of the two.
Finally, remember what is missing. Once you reach 73 or 75, the IRS sets a floor under your withdrawals whether you want the money or not, which the RMD calculator computes. Taxes reduce what each withdrawal actually delivers. And if you are drawing before 59½, the 72(t) rules constrain the amount as well.
Assumptions this model makes
- Withdrawals come at the start of each year. That is the conservative convention and matches how most retirees actually take income. Monthly withdrawals sit between the start-of-year and end-of-year cases and last very slightly longer.
- Returns are constant. No volatility, no sequence risk, no rebalancing. The single number you enter is earned every year.
- Withdrawals are the amount you take, not the amount you spend. Enter the gross figure if the account is tax-deferred, because income tax comes out of it.
- Guaranteed income is excluded. Enter only the spending your portfolio funds; Social Security and pensions should already be netted off.
- Spending is assumed constant in real terms. Actual retirement spending often eases in the middle years and rises again late, and no smooth model captures that.
- Fees come out of the return. Enter the return you expect after fund expenses and any advisory fee, because a 1% fee is a 1% reduction in i and moves the depletion date by years.
Level withdrawals hide the problem
Untick the inflation indexing and the projected longevity jumps, sometimes dramatically. That is not a better plan, it is a different one: you are choosing to let the purchasing power of your income decline. At 2.5% inflation, a payment held level for 25 years buys 46% less at the end than at the start. Use the level-withdrawal setting for a fixed annuity or a level pension, where the payment genuinely does not rise, and leave indexing on when you are modelling your own spending.
Other ways to ask the same question
This calculator solves the annuity equation for time. The same equation solved for the other variables answers the neighbouring questions, and it is usually worth running two of them together.
Solve for the payment and you get the maximum sustainable withdrawal, which is reported here as a supporting figure and treated in depth by the safe withdrawal rate calculator. Solve for the present value and you get the lump sum a given income requires, which is the retirement savings needed calculator. Solve for the rate and you get the return your plan implicitly demands, which is a useful sanity check against what a bond ladder actually yields.
There is also a structural answer to sequence risk that no deterministic model captures. Buying a lifetime income — an immediate annuity, or delaying Social Security to 70, which is the cheapest inflation-indexed longevity insurance most people can buy — converts a portfolio that might run out into an income that cannot. The trade is liquidity and bequest value for certainty. If you are working out whether your portfolio can bridge the years before a delayed claim, run this calculator over just the bridge period and check the balance at the end against the longer-horizon target for the remainder.