Savings Withdrawal Calculator, Explained

After reading this you will be able to predict how many months a savings balance lasts when you take out a fixed amount each month, and recognize when the interest alone covers your withdrawals so the money never runs out.

What this calculator answers

You have a pile of money in an account that earns interest. Every month you take some out. The balance shrinks because of the withdrawal but grows a little because of interest. This tool tracks that tug of war and tells you the month the balance hits zero, or reports that it never does.

Here is the hook. Suppose you hold 100000 at a 4% annual rate and withdraw 1000 a month. You might guess the money lasts 100 months, since 100000 divided by 1000 is 100. It actually lasts far longer, around 121 months, because interest keeps topping up the balance while you draw it down. That gap between the naive guess and the real answer is the whole point of the calculation.

When to use it, and when not

Use this when you have a known starting balance, a roughly fixed interest rate, and a fixed monthly withdrawal. It fits retirement drawdown planning, spending down an inheritance, or checking how long an emergency fund survives if you stop earning.

It is the mirror image of a savings plan where you add money each month. If you want to know how a balance grows with contributions instead of shrinking with withdrawals, use the Compound Interest Calculator. If you want the monthly saving needed to reach a target by a date, use the Savings Goal Calculator.

This model assumes a constant rate and a constant withdrawal. Real interest rates move, and real spending rises with inflation. A fixed 1000 withdrawal loses buying power over time, so a plan that looks safe here can still fall short in practice.

The formula and the intuition

Each month the balance changes in two steps. First it earns interest, then you remove the withdrawal. Let B_n be the balance after month n, let i be the monthly interest rate, and let W be the monthly withdrawal.

B_{n} = B_{n-1}(1 + i) - W

The monthly rate comes from the annual rate r by dividing by 12:

i = \frac{r}{12}

With r = 0.04 you get i = 0.003333, that is one third of one percent each month. The recurrence is easy to run month by month, and that is exactly what the tool does internally.

There is also a closed form. The number of months N until the balance reaches zero is:

N = \frac{-\ln\left(1 - \dfrac{i \cdot B_0}{W}\right)}{\ln(1 + i)}

Here B_0 is the starting balance, W is the withdrawal, and i is the monthly rate. The term i \cdot B_0 is the interest earned in the first month. If that interest is at least as large as W, the fraction inside the logarithm is zero or negative, the logarithm is undefined, and N is infinite. That is the mathematical version of living off the interest.

The break-even threshold

The single most useful number here is the withdrawal that exactly matches the first month of interest. Set the two equal:

W_{\text{break-even}} = i \cdot B_0

With B_0 = 100000 and i = 0.003333, the break-even withdrawal is 333.33 a month. Withdraw less than that and the balance grows every month, so it never runs out. Withdraw exactly that and the balance holds flat forever. Withdraw more and the balance declines, slowly at first, then faster as the shrinking principal earns less interest.

To find the break-even withdrawal for any balance, multiply the balance by the annual rate and divide by 12. At 4%, every 100000 supports about 333 a month indefinitely. At 6% it supports 500.

Reproducing the demo: 100000 at 4%, withdrawing 1000

These are the tool's default values, so you can click Calculate and check each line.

Convert the rate: i = 0.04 / 12 = 0.003333.
First month interest: 100000 \times 0.003333 = 333.33. Since 1000 is larger than 333.33, the balance falls, so the money is finite.
Balance after month 1: 100000 \times 1.003333 - 1000 = 99333.33.
Balance after month 2: 99333.33 \times 1.003333 - 1000 = 98664.44.
Apply the closed form: 1 - (0.003333 \times 100000 / 1000) = 1 - 0.3333 = 0.6667.
Then N = -\ln(0.6667) / \ln(1.003333) = 0.4055 / 0.003328 = 121.8 months.

So the balance lasts into the 122nd month, roughly 10 years and 2 months. Compare that with the naive 100 months (about 8 years and 4 months). Interest bought you an extra 21 months, more than a year and a half, on a balance you were spending down the whole time.

The balance falls in a gentle curve, not a straight line. Early on interest offsets much of the withdrawal, so the line is nearly flat. As the balance shrinks the interest shrinks with it, and the decline steepens toward the marker at month 121.8.

Reading and interpreting the result

The tool reports either a month count or the message that the balance lasts forever. Three cases cover everything.

Withdrawal below break-even: The balance grows every month and never runs out. With 100000 at 4%, any withdrawal under 333.33 lands here.
Withdrawal at break-even: The balance stays exactly flat. Interest and withdrawal cancel. This point is fragile: a small rate cut pushes you into decline.
Withdrawal above break-even: The balance runs down to zero in a finite number of months. The further above break-even you go, the sooner it ends, and the closer the answer gets to the simple division B_0 / W.

Notice why the curve steepens. In month 1 you earn 333 of interest, so the net drain is only 667. Near the end, when the balance is around 10000, interest is just 33, so the net drain is nearly the full 1000. The account empties faster as it empties.

Below the marker at 333.33 the balance never runs out (off the top of the chart). Just above it the duration is enormous and drops steeply, then flattens into a slow decline for large withdrawals. The values shown assume 4% and a 100000 start.

Common mistakes

The first mistake is dividing the balance by the withdrawal and stopping there. That ignores interest and always understates how long the money lasts. In the demo it gives 100 months instead of 122.

The second mistake is confusing the annual rate with the monthly rate. You must divide by 12 before running the recurrence. Using 4 as a monthly rate instead of 0.3333% would empty the account in a handful of months and mislead you badly.

The third mistake is treating the answer as a promise. The model holds the rate fixed, but a savings rate can drop from 4% to 2%, which cuts break-even from 333 to 167 and shortens every duration. If your withdrawal sat just below the old break-even, a rate cut can flip a "lasts forever" plan into one that runs dry.

The fourth is ignoring inflation. A fixed 1000 a month buys less each year. The calculator answers the question you asked in nominal terms; it does not adjust your spending upward, so real-world money runs out sooner if you increase withdrawals to keep pace with prices.

Related tools

To confirm the monthly rate you feed in, the APY / Effective Rate Calculator converts between nominal and effective annual rates. If you want to solve for a different unknown, such as the withdrawal that makes the money last a set number of years, the Time Value of Money Solver handles present value, payment, rate and term interchangeably. For the opposite direction, growing a lump sum toward a target, see the Savings Milestone Calculator or a fixed-term deposit in the Deposit / CD Calculator.

To see how much compounding matters at all, compare against the Simple Interest Calculator, and for a quick doubling estimate try the Rule of 72 Calculator. If your account credits interest continuously rather than monthly, the Continuous Compounding Calculator shows the small difference that makes.

Frequently asked questions

How long will 100000 last at 4% if I withdraw 1000 a month?

About 122 months, or roughly 10 years and 2 months. Without interest it would be 100 months, so the 4% return adds about 21 months.

What withdrawal lets my savings last forever?

Any amount at or below the monthly interest. Multiply the balance by the annual rate and divide by 12. For 100000 at 4% that is 333.33 a month.

Why does the balance fall faster near the end?

Interest is a percentage of the balance. When the balance is large it offsets much of the withdrawal, but as the balance shrinks it earns less, so more of each withdrawal comes out of principal.

Does the tool account for taxes or inflation?

No. It uses a fixed nominal rate and a fixed nominal withdrawal. Taxes on interest and rising prices both shorten how long the money really lasts, so treat the result as an upper bound on duration.

Is this the same as an annuity or amortization schedule?

The math is the same recurrence used for loan amortization, with your withdrawal playing the role of a loan payment against a balance that earns interest. That is why the Time Value of Money Solver can reproduce these numbers.

This is an educational estimate, not financial advice. Rates change, spending changes, and taxes apply. Talk to a qualified adviser before making decisions about your money.

Try it yourself in the tool