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Lump sum vs annuity: a present-value calculator
With a large lottery prize, the winner usually chooses between two options: the lump sum (cash option), received all at once, and the annuity, spread over many years. The big number in advertising is usually the annuity total, and the lump sum is much smaller. This page works out how the two are related and offers a calculator that compares present values using your own discount rate. All amounts are before tax, and nothing here recommends one option. For Korean lotteries see the lottery prize tax guide. US lottery taxes are not covered here.
The two Powerball choices
The official Powerball FAQ describes the annuity as "one immediate payment followed by 29 annual payments that increase by 5% each year". The prize chart calls it "30 graduated payments over 29 years". The cash option is "the amount of money required to be in the jackpot prize pool, on the day of the drawing" to fund the annuity prize. The FAQ says the annuity factor used to convert reflects interest rates on securities bought to fund the prize and that "the higher the interest rates, the higher the advertised" prize. And both advertised amounts are before federal and state tax.
The last sentence is the key point. An advertised $1.8 billion is not $1.8 billion in cash. It is the sum of 30 payments, and the cash available now is in the hundreds of millions. The draw of 24 December 2025 is an example: Powerball's announcement gave a jackpot of $1.817 billion and a cash option of $834.9 million, both before tax.
How the annuity schedule is built
Let the first payment be P, the yearly growth g = 5% and the number of payments n = 30. The total T is a geometric sum:
T = P × (1 + 1.05 + 1.052 + … + 1.0529) = P × (1.0530 − 1) ÷ 0.05 = P × 66.4388
So the first payment is about 1/66.4 (1.51%) of the total and the last is 1.0529 ≈ 4.116 times the first. For $1.817 billion, the first payment is about $27.35 million and the 30th about $112.57 million. These values are worked backwards so that the payments add up to the advertised total. We could not confirm from the official rules that real payments follow this formula exactly; it is a model built from the description above (5% growth, 29 further payments).
Comparing by present value
Money changes in value with time: a dollar today and a dollar in ten years are not the same. Turning future money into today's value gives the present value; at an annual discount rate r, money k years away is divided by (1 + r)k. Valuing the annuity above at different rates gives (first payment immediate):
| Annual discount rate | Present value of the annuity | Share of total |
|---|---|---|
| 0% | $1,817.0 million | 100.0% |
| 2% | $1,288.8 million | 70.9% |
| 3% | $1,099.4 million | 60.5% |
| 4% | $945.8 million | 52.1% |
| 5% | $820.5 million | 45.2% |
| 7% | $632.4 million | 34.8% |
The same annuity is worth $1.29 billion at 2%, $820 million at 5% and $632 million at 7%. Depending on the rate used, its value differs by nearly a factor of two.
The discount rate the cash option implies
With an advertised cash option you can reverse the calculation: the discount rate at which the annuity's present value equals the cash, the implied discount rate. For this jackpot the cash option of $834.9 million is 45.9% of the total, and the rate matching that ratio is about 4.87%. It can be read as a figure of the same kind as the FAQ's "interest rates on securities bought to fund the prize". We did not confirm from the official rules which securities these are or how the factor is set.
The number provides a benchmark. If your own discount rate is below 4.87%, the annuity's present value exceeds the cash option; above it, the cash is worth more. Your discount rate here is roughly the return you expect if you put the money elsewhere, and it only makes sense if it reflects inflation, investment risk and tax. This page does not decide which value is right.
Calculator
Change the structure, amounts and discount rate. The defaults are the December 2025 Powerball case above.
Mega Millions
From a search summary of the official Mega Millions site, the annuity is an initial payment followed by 29 annual payments, each 5% higher, 30 in all, and the cash option is the prize pool. The advertised annuity value is said to depend on that day's 30-year Treasury rate. We could not open the page ourselves, so this is partly verified. Since the structure matches Powerball, the Mega Millions choice in the calculator uses the same formula. How the two games differ in finer rules (timing of the first payment, rollover rules) we did not verify.
Korea's Pension Lottery 720+
Korea's pension lottery is an annuity from the start. According to Donghaeng Lottery, the first prize of Pension Lottery 720+ is KRW 7 million a month for 20 years, and the second prize and bonus KRW 1 million a month for 10 years. A single ticket's first prize is KRW 7 million × 20 years; a set adds KRW 4 million × 10 years. Payment is on the 20th of each month starting the month after the claim. The page says taxes are borne by the winner and withheld under the Income Tax Act.
| Annual discount rate | 1st prize (KRW 7 million × 240 months) | 2nd and bonus (KRW 1 million × 120 months) |
|---|---|---|
| 0% (nominal sum) | KRW 1.680 billion | KRW 120 million |
| 2% | KRW 1.384 billion (82.4%) | KRW 109 million (90.6%) |
| 3% | KRW 1.262 billion (75.1%) | KRW 104 million (86.3%) |
| 4% | KRW 1.155 billion (68.8%) | KRW 99 million (82.4%) |
| 5% | KRW 1.061 billion (63.1%) | KRW 94 million (78.6%) |
The nominal first-prize sum of KRW 1.68 billion has a present value of about KRW 1.26 billion at a 3% rate. The page does not mention a lump-sum option for these prizes, so the table is not for choosing but for seeing what the money is worth now. When setting such a prize beside a lump-sum prize of the same headline size (for example KRW 2 billion in Lotto 6/45), comparing the advertised nominal sum directly overstates the pension prize. For the tax treatment of annuity-type prizes see the tax guide.
How to choose a discount rate
- Opportunity cost: the benchmark is the yearly return you would expect from investing a lump sum safely. Assuming riskier investments raises the rate and makes the lump sum look better.
- Inflation: later annuity payments lose real value as prices rise. When inflation exceeds 5%, Powerball's 5% growth becomes a shrinking annuity in real terms.
- Timing of tax: a lump sum puts the income in one year and an annuity spreads it over several. Under progressive rates that difference can change the result. We did not check US tax law and have not included it.
- Personal circumstances: the recipient's age and health, estate plans and ability to manage assets are hard to turn into numbers but matter. From a search summary, Mega Millions says payments continue to a designated beneficiary or the estate if the winner dies; we did not check Powerball's rule.
Summary
- The advertised big number (the annuity total) is not money you receive now. In the Powerball case the cash option was 45.9% of the total.
- Which option is better depends on the discount rate; this calculator shows that relationship and draws no conclusion.
- Korea's Pension Lottery 720+ is an annuity by design, so its nominal sum should not be compared directly with a lump sum.
Limits
- All amounts are before tax and tax is not computed. An after-tax comparison of annuity and lump sum needs a separate check of tax law.
- The payment schedule is a model built from the description "5% growth, 30 payments". We could not confirm that real payments equal this formula.
- Lump-sum and annuity figures are estimates on the draw day, and Powerball's FAQ says final amounts can change with sales and the results of buying securities.
- Odds and expected return are not this page's subject. The expected value of one ticket in a rolled-over round is covered in the rollover ticket expected-value calculator.
This page is general education, not tax or legal advice. Tax rules change; check the cited statute or a licensed tax professional before acting.
Sources and verification
- Powerball FAQ: annuity = one immediate payment then 29 annual payments rising 5% a year; cash option = money required in the prize pool on draw day; annuity factor reflects interest rates on securities; both options before tax — verified
- Powerball prize chart: annuity paid in 30 graduated payments over 29 years, or lump sum — verified
- Powerball news, 25 Dec 2025: $1.817 billion jackpot, cash option $834.9 million, both before taxes (drawn 24 Dec 2025) — verified
- Mega Millions: annuity as an initial payment then 29 annual payments each 5% higher; cash value is the jackpot pool; annuity value depends on interest rates — partly verified · seen in a search summary of the official site; the page was not opened
- Donghaeng Lottery, Pension Lottery 720+: 1st prize KRW 7 million a month for 20 years, 2nd and bonus KRW 1 million a month for 10 years, paid monthly from the month after the claim, taxes borne by the winner and withheld under the Income Tax Act — verified
- LottoFlick calculator code (values pinned by tests) — computed by LottoFlick