Investment withdrawal calculator

What is an investment withdrawal calculator?

An investment withdrawal calculator — also called a drawdown or depletion calculator — answers a single retirement-planning question: if I keep taking a fixed amount out of a balance that is still earning a return, how long will the money last? You give it what you have today, the return you expect, how much you take out each period, and how often you take it. It reports the length of time before the balance reaches zero, or tells you the pot is self-sustaining and never runs out.

It is the mirror image of a savings projection. A future value calculator grows a balance forward while you pay money in; a withdrawal calculator runs the balance down while you take money out, netting each period’s withdrawal against the return the remaining balance earns.

How does the calculator work?

You provide a starting balance, an annual return rate, the amount of each withdrawal, and how often you withdraw (monthly, quarterly, or annually). The calculator converts the annual rate into a rate per withdrawal period, then works out how many periods the balance can sustain the withdrawal before it hits zero.

Each period two things happen: the balance earns a return, and you take a withdrawal out. If the withdrawal is larger than the return earned, the balance shrinks a little; repeat that and eventually it empties. If the withdrawal is smaller than or equal to the return, the balance never falls — you are living on the interest alone — and the calculator reports that it lasts indefinitely. The final period count is turned into a natural-language duration such as “10 years and 2 months”.

Formula

With a starting balance $PV$, a withdrawal $PMT$ taken each period, and a return $r$ per period, the number of periods $n$ until the balance is exhausted is:

$n = -\frac{\ln\!\left(1 - \dfrac{PV \cdot r}{PMT}\right)}{\ln(1 + r)}$

Where:

• $PV$ is the starting balance.
• $PMT$ is the amount withdrawn each period.
• $r$ is the return rate per period.
• $n$ is the number of withdrawal periods the balance lasts.

The periodic rate comes from the annual rate and the number of withdrawals per year $k$ (12 for monthly, 4 for quarterly, 1 for annual):

$r = \frac{\text{annual rate}}{100 \cdot k}$

When the balance never depletes

The quantity $PV \cdot r$ is the return the balance earns in one period. If the withdrawal does not exceed it, the balance is self-sustaining:

$PMT \le PV \cdot r \;\Rightarrow\; \text{lasts indefinitely}$

Mathematically the term inside the logarithm becomes zero or negative and $n$ is undefined, which is the calculator’s cue to report an indefinite lifespan.

Zero return rate

When the return is zero the formula would divide by zero, so it collapses to a plain division — the balance is simply shared out evenly across the withdrawals:

$n = \frac{PV}{PMT}$

Examples of use

1. A balance of 100,000 earning 4% a year, with 1,000 withdrawn at the end of every month:

   • Starting balance $PV$ = 100000
   • Periodic rate $r = \dfrac{4}{100 \cdot 12} \approx 0.0033333$
   • Withdrawal $PMT$ = 1000

   Because $PV \cdot r = 333.33$ is smaller than the 1,000 withdrawal, the balance depletes:

   $n = -\frac{\ln\!\left(1 - \dfrac{100000 \cdot 0.0033333}{1000}\right)}{\ln(1.0033333)} = -\frac{\ln(0.66667)}{0.0033278} \approx 121.8 \text{ months}$

   That is about 10 years and 2 months, and the total withdrawn over that time is roughly $1000 \times 121.8 \approx 121{,}842$.

2. The same 100,000 balance earning 6% a year, but withdrawing only 400 a month:

   • Periodic rate $r = \dfrac{6}{100 \cdot 12} = 0.005$
   • Return earned each month $PV \cdot r = 100000 \times 0.005 = 500$

   The 400 withdrawal is less than the 500 earned, so the balance actually grows rather than shrinks. The calculator reports that the balance lasts indefinitely.

Practical notes

• The result assumes a constant return every period. Real markets do not deliver a steady rate, and a run of poor early returns (sequence-of-returns risk) can empty a balance far faster than the average rate suggests.
• Withdrawals here are in nominal terms. If you need the same purchasing power each year, increase the withdrawal for inflation and treat the return as a real (after-inflation) rate.
• The break-even point is where the withdrawal equals the return earned, $PMT = PV \cdot r$. Withdraw a shade less and the balance survives forever; a shade more and it will eventually run dry.
• A rough guide many planners start from is withdrawing about 4% of the starting balance per year — deliberately below typical long-run returns so the pot lasts through a long retirement.

FAQs

What does “lasts indefinitely” mean?

It means the withdrawal is small enough that the return the balance earns each period covers it, so the balance never falls to zero. You are effectively spending only the growth and leaving the capital intact.

Should I use a nominal or a real return rate?

Use whichever matches your withdrawals. If your withdrawal amount is fixed in today’s money and never rises, a real (inflation-adjusted) return keeps the projection honest. If the withdrawal itself grows with inflation, model that separately — a single fixed withdrawal cannot capture it.

Why is the answer shorter than dividing the balance by the withdrawal?

Only when the return is zero does the balance last exactly $PV / PMT$ periods. With a positive return the earnings extend the lifespan, so the balance lasts longer than a plain division — unless the withdrawal is so large it swamps the return, in which case the two figures are close.