Retirement withdrawal calculator and formula

Enter the pot you start with, the return you expect it to earn, and the amount you take out every month. It returns the month the money runs out, the balance left at a horizon you choose, and the growth the pot earned across that same horizon while you were spending from it.

That growth line is not a slice of the balance sitting beside it. In the first example below the pot ends on $123,219.14 having earned $343,219.14, because everything it earned left again as withdrawals, and part of the original pot went with it. The lines add rather than nest: what you started with, plus the growth, less what you took out, leaves the balance.

Two things happen to the pot at once and they pull in opposite directions. The balance earns a return, which pushes it up, and the withdrawal comes out, which pushes it down. Whichever is larger decides the direction, and once the withdrawal is the larger of the two that direction never reverses: the balance falls, the return earned on a smaller balance falls with it, and the gap between them widens every month. That is why a pot being drawn down empties slowly at first and then all at once.

The final withdrawal is almost always a short one, because the balance rarely lands exactly on zero at the end of a month. This page reports the month in which the pot cannot pay a full withdrawal, which is the month the money is gone.

Each period does two things in order: the balance earns its return, then the withdrawal leaves. Repeat that $n$ times and what remains is:

$$B_n = P(1 + i)^n - W \times \frac{(1 + i)^n - 1}{i}$$

The first term is the pot you started with, left alone. The second is what your withdrawals would have grown into had they stayed invested. The pot runs out at the moment the second term catches the first, which is later than most people guess: compound interest keeps working on whatever is still there, so as long as the pot earns anything at all it lasts longer than the balance divided by the withdrawal.

Set $B_n$ to zero and solve for the number of periods:

$$n = \frac{\ln\left(\frac{W}{W - iP}\right)}{\ln(1 + i)}$$

That bracket only means anything while $W$ is larger than $iP$, which is the return the pot earns in a single period. Take exactly $iP$ and the balance holds level forever. Take less and it climbs. In both cases there is no answer to give, because there is no such month. In the first example below the pot earns 5 percent a year while the withdrawals take out 7.2 percent of the starting balance, so the balance falls.

One convention sits inside that division. Dividing the annual figure by 12 treats it as a nominal annual rate, so twelve months of 0.4167 percent compound to 5.12 percent across the year rather than 5 percent, and 3 percent divided by 12 compounds to 3.04 percent. Enter a figure already quoted as a nominal annual rate and the arithmetic matches the quote exactly. Enter a compound annual return of 5 percent as 5 and the page runs a little generous, because the monthly rate that truly compounds to 5 percent is 0.4074 percent, which empties the same pot at month 280 instead of month 286. The APR against APY calculator converts between the two.

This page applies the same return every single month. Markets do not, and a pot being drawn down is unusually sensitive to that difference.

The reason is order. A withdrawal made after a fall sells a larger share of the pot than the same withdrawal made after a rise, and the shares sold are not there for the recovery. Two return sequences with an identical average, run against the same pot and the same withdrawal, do not end in the same place. A drawdown in the first years of a plan therefore costs more than the same drawdown in the last years, which is not true of a pot nobody is spending from.

That is what a fixed withdrawal rate is: a planning rule built on assumptions about returns, about how long the money has to last, and about what the pot holds. It is not a guarantee, and no rate is safe in every sequence of returns that could actually turn up. Use the numbers here to see the shape of a plan and how far it moves when one input changes. This is educational material rather than financial advice.

Every extra dollar a month is income you get now, paid for out of the far end of the plan. Every dollar you hold back is income you forgo now in exchange for room to absorb a poor decade. There is no setting that gives you both, and that trade is the whole decision.

The examples below show how sharp the exchange rate is. At 5 percent, $3,000 a month from $500,000 still leaves $123,219.14 after 20 years and lasts into year 24. At 3 percent, the same pot and the same withdrawal are gone 18 years in. Two percentage points of return moved the end of the plan by almost six years, and nothing about the spending changed.

Inflation pulls in the same direction. The withdrawal here is flat in cash terms, so what it buys shrinks a little every year. Keeping the buying power level means raising the withdrawal annually, which empties the pot sooner than this page shows. One way to see it in today's money is to enter a return net of inflation: the real return calculator works that figure out, and inflation and purchasing power explains the erosion. Running the same arithmetic in the other direction, filling a pot rather than spending one, is the savings goal calculator.