The Commons · billboard versus bank
The Pot That Was Never Cash
The billboard says $1.25 billion. The cash a Powerball winner could actually take on December 17, 2025 was $572.1 million: 45.77 percent of the headline. The advertised jackpot was never a pile of money. It is the arithmetic sum of 30 graduated payments, one now and 29 more a year apart, each 5 percent larger than the last, and the cash option is simply that stream discounted to today. Roughly half the headline goes missing not to any fee or tax but to the time value of money, and the exact gap is an implied return near 4.9 percent.
So the real question is not "lump or annuity." It is can you beat about 4.9 percent, guaranteed, after tax, and net of the risk of not earning it? Above that line the lump wins in present value; below it the annuity does. Drive the sandbox: watch the billboard number decompose into 30 growing bars that add up to it, then turn the discount-rate dial and watch the verdict flip on a line your own rate sits above or below.
On the billboard (annuity sum)
$1.25B
the sum of 30 payments over 29 years
45.77%
of headline
In the bank (cash option)
$572.1M
the present value the lottery would pay today
Your discount rate is parked exactly on the annuity's implied rate, so the cash option and the discounted stream are worth the same today. Move the rate dial to break the tie.
The staircase that adds up to the billboard
30 payments, the first paid immediately, each 5 percent taller than the one before. Their heights add up to exactly the advertised jackpot. The headline is a total, not a pot.
A bar chart of 30 annual payments growing 5 percent each year, from the immediate first payment to the largest final payment, whose heights sum to the advertised jackpot.
Discounted to today: the annuity stream vs the cash option
The 30 payments discounted at your rate, beside the lump the lottery pays today. Whichever bar is longer is the better deal in present value.
Cash as a fraction of the headline
45.77%
cash value / advertised jackpot
Annuity's implied rate (the crossover)
4.90%
beat this after tax and the cash wins
First → last payment
$18.8M → $77.4M
immediate, then 29 growing 5% a year
Two different games, same structure. Switch to confirm the missing half is not a one-off.
The after-tax, after-risk annual return you believe you can reliably earn. This is the rate you must beat, guaranteed, to make the lump the better present-value deal.
24% is only what is withheld. 37% is the true top marginal rate on a nine-figure prize. The roughly 13-point gap is owed at filing.
Deliberately coarse. State treatment varies: nine states levy no income tax, several (including California) exempt lottery winnings entirely, New York tops out near 10.9% with a New York City add-on of 3.876%.
At the published cash value this solves to about 4.90% for the December 2025 Powerball drawing. Crank it up and the cash option shrinks toward 40 percent of the headline; pull it toward zero and it swells past 60. "The cash is about half" is not a constant, it is whatever interest rates make it, which is why older jackpots quoted about 60 percent and this 2025 one quotes about 46.
Where the other half went
Slide the funding-rate dial and watch the cash option move while the billboard number stays frozen. Nothing has been taken away. The advertised jackpot is genuinely paid, in full, if you let the state send you 30 checks over 29 years. The gap between the headline and the cash is not a fee, not a penalty, and not the tax. It is the time value of money: a dollar promised in 2054 is worth less today than a dollar in hand, because the dollar in hand can be invested. Discount 30 growing payments back to the present and you get roughly half the sum. The lottery does not keep the difference; it never existed as cash. To fund the annuity, the lottery buys a ladder of U.S. Treasury STRIPS that mature on the payment dates, and the cash option is what that ladder costs today.
That is why the fraction tracks interest rates. When Treasury yields are high, the lottery needs less principal to buy the same future checks, so the cash option is a smaller slice of the headline. When yields are low, it needs more, and the slice grows. The 45.77 percent on the December 2025 billboard is a 2025 number. In the low-rate years around 2015 the same structure paid closer to 60 percent.
The answer is a line your own rate sits on
The crossover flip, and it cuts both ways
The lump beats the annuity in present value only if your personal discount rate exceeds the annuity's implied rate, about 4.9 percent for this drawing. Above the crossover, the cash grown at your rate out-earns the 30 payments, and the verdict chip reads TAKE THE CASH. Below it, the guaranteed graduated stream is worth more today than the lump, and the chip flips to TAKE THE ANNUITY. At exactly the implied rate the two are worth the same. The crossover is not a matter of opinion. It is the annuity's implied return, solved from the drawing, and the whole job of the sandbox is to let you move your rate across that line and watch the verdict change. So the honest framing is not "lump good, annuity bad." It is a question about you: can you beat about 4.9 percent, guaranteed, net of tax and net of the risk of not actually earning it?
The tax layers are real, layered, and do not cleanly favor either side
Both options are fully taxable, but differently. The lump drops the entire cash value into one tax year, so essentially all of it is taxed at the 37 percent top federal marginal rate. The annuity spreads the income across 29 years, yet because each annual payment is itself tens of millions, each one also lands in the top bracket. So the celebrated "the annuity keeps you in a lower bracket" saving is far smaller than winners imagine, and a flat top-rate tax barely moves the crossover, because it shrinks both sides by the same fraction. Flip the federal toggle to 37 percent and watch: the mandatory 24 percent withholding was never the final bill. On this drawing's cash value, 24 percent withheld is about $137.3M, but the true 37 percent liability is about $211.7M, so roughly $74.4M is owed at filing. State tax is a genuine wildcard we name and refuse to fake: it runs from 0 percent (nine states levy no income tax, and several, including California, exempt lottery winnings) up to about 10.9 percent in New York, plus New York City's 3.876 percent local add-on. These are labeled scenarios with the jurisdiction stated, never one canonical take-home.
The math case for the lump and the behavioral case for the annuity are both real
The present-value case for the lump silently assumes things the arithmetic cannot guarantee: that you will actually earn your assumed rate, that you will not be defrauded, and that you will not spend the principal. The annuity is best understood as ruin insurance: an income you cannot blow, borrow against into oblivion, or be talked out of by relatives and advisers, funded by default-free Treasuries. So the complete answer is a split decision. The lump wins for a disciplined winner who can reliably beat about 4.9 percent after tax. The annuity wins for everyone honest enough to doubt that they are that person. (The widely repeated "about a third of winners go broke" line is a contested magnitude, weakly sourced. Treat the ruin risk as real without leaning on a hard number.)
The two, side by side
| Take the cash (lump) | Take the annuity | |
|---|---|---|
| What you receive | One payment now: the present value | 30 graduated payments over 29 years, summing to the headline |
| Fraction of the billboard | About 46% (2025 rates); rate-dependent | 100% of the advertised sum, but spread out |
| Wins in present value when | You can beat the implied ~4.9% after tax | You cannot reliably beat ~4.9% after tax |
| Federal tax | All of it in one 37% year (24% withheld) | Each payment still lands in the 37% bracket |
| Main risk | You blow, over-borrow, or are defrauded of it | Inflation and illiquidity; default risk is near zero (Treasury-funded) |
| Best described as | Freedom, if you are disciplined | Ruin insurance you cannot spend at once |
The check: every number recomputed in front of you
Nothing here is a stored lookup. For the current drawing and dial settings the page rebuilds the whole schedule and discounts it from the same equations the offline verifier uses, live:
The offline gate recomputes all of it and exits 0 only if every check passes: node research/lottery-lump-sum-or-annuity/verify-lottery-lump-sum-or-annuity.mjs. Free choices & scope. The structural rules are fixed and sourced: 30 payments, the first immediate, each 5 percent larger than the last, summing to the advertised jackpot; the cash option is the present value of that stream. The two bundled drawings and their advertised/cash pairs are real, dated, official figures printed above and pinned in the sources. The implied rate is solved from each drawing, not quoted, so it is specific to that drawing and its date; it tracks Treasury yields and is not a fixed 4.9 percent. Taxes are named scenarios, federal-only unless you add a state rate, and never a single canonical after-tax number: 24 percent is withheld, 37 percent is the top marginal rate, and state tax ranges 0 percent to about 10.9 percent plus local add-ons. The lump-versus-annuity verdict is a present-value comparison; it is not tax, estate, or investment advice.
What is exactly true here, and what is a named choice
Exactly true (the sourced structure). The advertised jackpot is the annuity sum: 30 payments, one immediate and 29 annual, each 5 percent larger than the last, adding up to the headline (Powerball and Mega Millions use the identical structure). The cash option is the present value of that stream, the lump the lottery would otherwise use to buy it via U.S. Treasury STRIPS. For Powerball's real drawing of December 17, 2025 the advertised jackpot was $1.25 billion and the published cash value was $572.1 million, so the cash was 45.77 percent of the headline. Solving for the discount rate that turns the 30-payment schedule into $572.1 million today gives an implied rate of about 4.90 percent. The cash fraction is a strictly decreasing function of the funding rate, so no fixed "50 percent" is correct across years.
Named choices and scope. The bundled drawings are two real, dated, official pairs; the "your rate" and "funding rate" dials are yours to set. The tax layer is a set of labeled scenarios, not a precise take-home: applying a flat combined rate to both sides is a deliberate simplification that makes the honest point (a flat top-bracket tax barely moves the crossover) without pretending to compute one person's real bill across 29 years of brackets, deductions, and changing law. State tax is coarse and jurisdiction-specific. The "about a third of winners go broke" trope is treated as a real but contested risk, not an established percentage.
Not modeled. Year-by-year bracket stacking on the annuity, the gift and estate consequences of either choice, inflation adjustment of the payments beyond the built-in 5 percent growth, state lottery-specific withholding, and any change in tax law over the payout period. None of these change the reversal at the heart of the page: the billboard number is a summed staircase, and cash-versus-annuity is a crossover your own discount rate flips.