Understanding how long your savings last
The table varies the withdrawal on the worked example's $100,000 balance at 5%, showing how sensitive the horizon is near the perpetuity threshold of $416.67 per month.
| Monthly withdrawal | Outcome for $100,000 at 5% |
|---|---|
| $400 (below $416.67 interest) | Never depletes — interest alone covers the withdrawal |
| $600 | Lasts about 23.8 years |
| $1,000 | Lasts about 10.8 years (129.6 months) |
| $2,000 | Lasts about 4.7 years |
- The "neverDepletes" verdict means the withdrawal is at or below the monthly interest (balance × rate ÷ 12); the balance holds steady or grows, and the monthly-interest result shows the income the balance generates.
- The model assumes a constant rate and a fixed withdrawal; real returns fluctuate, and sequence-of-returns risk means volatile portfolios can deplete faster than a constant-rate model suggests even with the same average return.
- Withdrawals are not adjusted for inflation here — a fixed $1,000 buys less each year, so maintaining purchasing power requires growing withdrawals, which shortens the horizon.
- Interest earned in taxable accounts is taxable; the model uses gross figures. Educational estimate only, not financial advice.
What is a savings withdrawal plan?
A savings withdrawal plan (sometimes called a systematic withdrawal or decumulation plan) draws a fixed amount from a savings or investment balance each month while the remaining balance continues to earn a return. It is the standard framework for questions like how long a retirement nest egg, severance payment, or sabbatical fund will last at a given spending rate.
The mathematics is the annuity-depletion equation — the mirror image of loan amortization. Each month the balance earns interest and then loses the withdrawal; the balance falls only by the amount the withdrawal exceeds the interest. In the worked example, $100,000 at 5% earns $416.67 in the first month, so a $1,000 withdrawal reduces the balance by only $583.33 initially. The gap widens as the balance shrinks, which is why depletion accelerates toward the end.
There is a sharp threshold in this arithmetic: if the monthly withdrawal is less than or equal to the interest the balance earns each month (balance × rate ÷ 12), the balance never falls — the plan is perpetual, and the calculator reports a "neverDepletes" verdict along with the monthly interest figure instead of a finite horizon.
How to use this savings withdrawal calculator
- Enter the starting balance you will draw from.
- Enter the fixed amount you plan to withdraw each month.
- Enter the annual interest or return rate the remaining balance earns.
- Read how many months and years the balance lasts and the total amount withdrawn — or, if the withdrawal is at or below the monthly interest, the "neverDepletes" verdict and the monthly interest that covers it.
- Worked example: $100,000 earning 5% with $1,000 withdrawn monthly lasts about 129.6 months — roughly 10.8 years — during which about $129,628 is withdrawn. Without any interest, the same plan would last only 100 months.
The formula behind savings depletion
The number of months until depletion solves the annuity equation for n: the month at which the future value of the balance, minus the future value of the withdrawal stream, reaches zero. Rearranged, n = −ln(1 − P·r/W) ÷ ln(1 + r), where P is the balance, W the monthly withdrawal, and r the monthly rate. With a 0% rate the formula reduces to simple division, n = P ÷ W.
The expression inside the logarithm shows the perpetuity threshold directly: when P·r ≥ W — interest covers the withdrawal — the argument of the logarithm is zero or negative, no finite n exists, and the balance lasts forever. The calculator detects this case and reports it as a verdict rather than a number.
Common mistakes
- Estimating longevity as balance ÷ withdrawal, ignoring interest — that shortcut gives 100 months in the worked example versus the true 129.6.
- Overlooking the perpetuity threshold: at or below balance × rate ÷ 12 per month, the plan is sustainable indefinitely, which changes the decision entirely.
- Treating a volatile investment return like a fixed interest rate — a bad early sequence of returns depletes a real portfolio faster than the constant-rate math implies.
- Ignoring inflation, which erodes what a fixed withdrawal buys by roughly a quarter over ten years at 3% inflation.
- Forgetting taxes on interest or on retirement-account withdrawals, which reduce the net amount actually available to spend.
Часто задаваемые вопросы
How long will $100,000 last with $1,000 monthly withdrawals?
At a 5% annual return, about 129.6 months — roughly 10.8 years — because the remaining balance keeps earning interest that partially offsets each withdrawal. With no interest at all it would last exactly 100 months. Total withdrawals over the period come to about $129,628, nearly $30,000 more than the starting balance, funded by the interest earned along the way.
Why does the calculator say my savings never deplete?
Because your monthly withdrawal is at or below the interest the balance earns each month. For $100,000 at 5%, monthly interest is $416.67; any withdrawal up to that amount is covered by earnings alone, so the principal never falls. This is the perpetuity condition W ≤ P × r — mathematically, no finite depletion time exists, and the calculator shows the monthly interest instead.
What withdrawal amount makes savings last forever?
Any amount up to the monthly interest: balance × annual rate ÷ 12. On $100,000 at 5% that is $416.67 per month. Withdrawing exactly the interest keeps the nominal balance constant, though inflation still erodes its real value over time — a perpetual nominal balance is not a perpetual standard of living.
Does this work for retirement planning?
It models the core arithmetic — a balance earning a return while funding fixed withdrawals — which is the skeleton of retirement decumulation. Full retirement planning adds inflation-adjusted spending, variable market returns, sequence-of-returns risk, taxes, and longevity uncertainty, which is why research such as the Trinity study examines historical success rates of withdrawal strategies rather than a single constant-rate projection.
How does the interest rate change how long savings last?
Substantially, and non-linearly. $100,000 with $1,000 monthly withdrawals lasts 100 months at 0%, about 129.6 months at 5%, and never depletes once the rate reaches 12% (where monthly interest is $1,000). The closer the withdrawal is to the interest earned, the more sensitive the horizon becomes to small rate changes — near the threshold, a fraction of a percent can add years.
Источники
- Consumer Financial Protection Bureau (CFPB). Planning for retirement — managing retirement income. consumerfinance.gov.
- Cooley PL, Hubbard CM, Walz DT. Retirement Savings: Choosing a Withdrawal Rate That Is Sustainable. AAII Journal, 1998 (the Trinity study).
- Bengen WP. Determining Withdrawal Rates Using Historical Data. Journal of Financial Planning, 1994.
- Ross SA, Westerfield RW, Jordan BD. Fundamentals of Corporate Finance. 13th ed. McGraw-Hill Education, 2021 — annuity mathematics.