Withdrawals remove money that could otherwise keep growing
A withdrawal changes compound growth by reducing the amount left to earn future returns. The question is not answered by calculating an untouched ending balance and subtracting total withdrawals afterward, because that shortcut leaves withdrawn money earning returns for too long. Each withdrawal needs a place in the timeline, with a clearly stated amount and periodic growth assumption.
This guide uses a constant positive rate to explain that arithmetic. It does not recommend a withdrawal amount, assess retirement spending or guarantee that an investment will last. Real returns, fees, inflation and cash needs can vary. A transparent illustration must retain those limits instead of presenting one smooth curve as a financial sustainability test.
Write the end-of-period recurrence first
Let B_k be the balance after period k, i the rate per period and W the withdrawal made at each period end. Then B_k = B_(k−1) × (1 + i) − W. Starting with $10,000, a hypothetical monthly rate of 0.5 percent and a $200 end-month withdrawal gives $9,850 after the first month and $9,699.25 after the second.
Those rows first credit $50 and then $49.25 of modeled interest before the respective withdrawals. A monthly rate of 0.5 percent corresponds to a 6 percent nominal annual rate with monthly compounding, not exactly 6 percent effective annual yield. Keep that convention explicit when comparing with another calculator or a quoted savings yield.
Use the closed form only with its matching assumptions
For N equal periods and i not zero, the end-withdrawal formula is B_N = P × (1 + i)^N − W × [(1 + i)^N − 1]/i. The second term is the future-value effect of all withdrawals, not merely the total dollars paid out. With the example's P = $10,000, i = 0.005, W = $200 and N = 12, the result is approximately $8,149.67.
Total withdrawals are $2,400. The identity ending balance + withdrawals − opening balance gives modeled earnings of about $549.67. It is not correct to call the $1,850.33 decline in account balance the full investment loss, because money was deliberately taken out. Preserve both the withdrawals and the remaining balance when reconciling the result.
Move the withdrawal earlier and recalculate the growth exposure
If the same $200 is withdrawn at each period beginning, use B_k = (B_(k−1) − W) × (1 + i). The first month ends at $9,849 instead of $9,850 because one dollar of interest on the withdrawn $200 is no longer earned. In the closed form, multiply the withdrawal-series term by an additional factor of 1 + i.
After twelve periods under that beginning-withdrawal convention, the example ends at approximately $8,137.33. The total withdrawals are unchanged, but their timing reduces the balance by about $12.34 relative to the end-month case. This timing comparison assumes the full withdrawals can be made when scheduled and does not authorize drawing an account below its available funds.
Check zero-rate and interest-only boundaries
At a zero rate, the formula becomes B_N = P − N × W. Dividing by i in the positive-rate formula is then invalid, even though the cash ledger remains simple. For the example, twelve $200 withdrawals at zero growth leave $7,600. Use this as a check that the positive-rate answer and its reported earnings reconcile sensibly.
At a positive constant rate, an end-period withdrawal equal to P × i leaves the opening balance unchanged in this ideal model. A larger withdrawal reduces it. This is an algebraic boundary, not a safe withdrawal rule: variable returns, inflation, fees or taxes can invalidate an apparently stable real-world spending plan even when a chosen constant-rate worksheet preserves a nominal balance.
Stop at depletion rather than displaying fictitious borrowing
With $10,000, 0.5 percent monthly growth and $200 end-month withdrawals, the closed-form balance reaches zero at approximately 57.68014 theoretical periods. The monthly ledger supports 57 full withdrawals but not a complete 58th withdrawal without another source of funds. At the next payment date, the available amount must be checked and any final withdrawal limited to what the model actually has.
A negative balance from extending the formula is not automatically an approved overdraft or loan. The arithmetic continuation has crossed the funded-plan boundary. Keep any final partial withdrawal separate and do not claim that a fractional solution represents an actual continuous payment event. The observation period, event timing and available balance determine the discrete cash record.
Use a separate worksheet rather than a negative deposit input
NumUtility's current Compound Interest Calculator accepts nonnegative recurring deposits. It does not implement withdrawals, a final partial payout or a depletion schedule. Do not enter a negative contribution as though it were a supported feature. You can use its zero-deposit scenario to inspect untouched growth, but that alone does not reproduce this withdrawal path.
A separate row-by-row worksheet can carry opening balance, growth, planned withdrawal, permitted actual withdrawal and closing balance. An FV expression can verify the constant-rate closed form before depletion if cash-flow signs and timing are correct. After that boundary, use the capped ledger rather than treating an unconstrained financial-function output as spendable money. If the account has a minimum payout or a withdrawal fee, keep that separate from the requested cash amount; otherwise the modeled withdrawal and the amount reducing invested assets need not coincide.
Separate a teaching model from uncertain investment outcomes
Record whether the chosen rate represents a nominal compound-interest convention or an effective periodic growth assumption. Include withdrawal dates and specify whether costs or taxes are excluded. If modeling actual variable returns, apply them in their sequence; their order can matter when withdrawals occur. A constant average is not a complete substitute for that path.
This educational article does not supply investment or retirement advice. Its result is conditional on a fixed rate, equal periods and the stated withdrawal timing. For a spending decision, relevant risks and contractual account restrictions require separate consideration. The useful calculation is the complete balance and payout record, including the point where an assumed withdrawal becomes unavailable.