Case studies · 2025
The Loto-Quebec lottery choice
A real lottery winner's choice between a lump sum and payments for life is used to teach compounding, the zero curve and duration.
What happened
A prize with two prices
The choice at the centre of this case is built into the game itself. Loto-Quebec's "Gagnant a vie" ("Winner for Life") scratch card has long offered the same top prize: three matching "piggy bank" symbols win either $1,000 a week for the rest of the winner's life, or a one-time lump sum of $1,000,000. The ticket costs $5, and the odds of hitting that top prize are 1 in 1,200,000. Most players never have to weigh the choice. In 2025, one did.
The win
Brenda Aubin-Vega, a young woman from Montreal, scratched two tickets during a break at work and uncovered the winning combination. Loto-Quebec confirmed the win in a press release on 3 July 2025, naming the store where she bought the ticket, Depanneur Jen & Dan on Rue Poirier, and noting the retailer's commission on the sale: $10,000, or 1% of the prize's headline value. Loto-Quebec's own release describes her only as "a woman in her twenties" ("dans la vingtaine"); several English-language outlets, including Yahoo News Canada and Yahoo Finance, later reported her age as 20, and that figure has stuck in most subsequent coverage.
The choice, and the argument it started
She was offered the standard choice: take the $1,000,000 now, or take $1,000 every week for the rest of her life. She chose the weekly payments. The story spread quickly, first through Quebec newswires and CTV News Montreal, then into English-language personal-finance coverage, and it split opinion the way any "cash or annuity" question does online. The arithmetic commentators reached for was simple: $1,000 a week comes to $52,000 a year, and it would take about 1,000 weeks, roughly 19 years, of payments to match the $1 million she turned down, undiscounted. Some framed her choice as locking in a "5.2% yield" on the money she left on the table; others called it the safer, smarter pick. Both framings capture only half the story, since neither states what a dollar received in year 30 is worth today. That question is exactly what a zero curve answers, and it is the question this case is built to resolve properly.
The fine print
Loto-Quebec's own rules document is more specific than any news report about what the winner actually holds. The annuity is paid net of tax through a designated insurance company, and it carries an inheritance clause: if the winner dies within 20 years of claiming the prize, her heirs continue to receive the payments for whatever remains of those 20 years. If the winner is 71 or older at the time of the claim, a different rule applies, tied to Canada's Income Tax Act, that caps payments to heirs at what would have been the winner's 91st birthday. None of that changes the underlying valuation question. It only fixes exactly what stream of cash flows is being valued.
The mechanics, in course language
This case is not a firm using a derivative contract. It is a plain, easy-to-follow version of a problem every bond desk faces: turning a stream of future cash flows into a single price today.
Comparing "$1,000 a week" with "$1,000,000 today" first requires fixing what "a week" and "for life" mean in growth-factor terms, the same issue that arises when comparing two banks quoting different compounding frequencies. Once that is fixed, the weekly annuity is simply a bundle of future cash flows, and pricing it means discounting every one of those payments back to today using a rate appropriate to its horizon. That is exactly what a zero curve gives for any bond or swap cash flow. Under a flat long-run discount rate, the weekly-for-life stream behaves like a long-dated, high-coupon bond, or a level perpetuity cut off at a life-expectancy horizon. Its value moves with the assumed rate, just as a bond's price moves with its yield, and because the payments run for decades, that sensitivity, its duration, is large.
Seen this way, choosing the annuity is equivalent to holding a very long-duration, fixed cash-flow asset. Choosing the lump sum is equivalent to holding cash instead, free to reinvest at whatever rate the future brings. A breakeven discount rate exists at which the two choices are worth exactly the same, and landing on one side of that breakeven is an implicit bet on where interest rates will sit for the rest of the winner's life. Orange County's 1994 loss, covered elsewhere in this course, makes the same point at institutional scale: a breakeven or forward rate is a price the market is willing to trade at, not a forecast, and betting against it is a real position with real risk.
Data and facts
| Quantity | Value | Source |
|---|---|---|
| Lump-sum choice | $1,000,000, non-taxable | Loto-Quebec, official game rules |
| Annuity choice | $1,000/week for life, net of tax | Loto-Quebec, official game rules |
| Ticket cost | $5 per play | Loto-Quebec, official game rules |
| Odds of the top prize | 1 in 1,200,000 | Loto-Quebec, official game rules |
| Weekly-to-annual conversion | $1,000/week ≈ $52,000/year | Recomputed: 1,000 × 52 |
| Undiscounted 60-year total | about $3.1M | Course figure, matches recomputation |
| Present value at a flat 3% (60-year horizon) | about $1.45M | Course figure, matches recomputation |
| Breakeven discount rate | ≈5% (4.93% precisely) | Course figure, matches recomputation |
| Duration of the stream (at 3%) | ≈21 years | Course figure, matches recomputation |
| Retailer commission on the sale | $10,000 (1% of prize value) | Loto-Quebec press release, 3 Jul 2025 |
| Quebec lifetime-annuity winners since start of 2025 | 10 (9 weekly, 1 annual) | Loto-Quebec press release, 3 Jul 2025 |
Take the 3% flat long-end rate and the 60-year collection horizon below as teaching assumptions, chosen to make the arithmetic concrete, not as Loto-Quebec's own numbers. Loto-Quebec does not publish the actuarial basis it uses to price the annuity, so treat what follows as a worked illustration of the method, applied to this case, rather than a reconstruction of the operator's own valuation.
The lesson
- A quoted cash-flow stream and a lump sum are only comparable once you fix a discount rate. Change the rate and the "obviously better" choice can flip, which is exactly why a zero curve, not a single number, is the right way to price money over time.
- "She was foolish" and "she was smart" are both incomplete claims. The honest statement is conditional: at a flat 3% long-run rate, the annuity was worth more than the $1 million; above roughly 5%, the lump sum would have been worth more.
- Long-dated cash-flow streams have long duration, so their value is highly sensitive to the discount-rate assumption. A "safe" choice like a lifetime annuity still carries real interest-rate risk, just expressed as valuation risk instead of default risk.
- The same mathematics that prices a 60-year lottery annuity prices a government bond, a swap or a pension liability. The lottery version is memorable because the stakes are personal and the numbers are small enough to work out by hand.
Where it appears in the course
Think about it
- If the discount rate you believe in is 4%, closer to the breakeven than the course's 3% assumption, does the annuity still beat the lump sum? By how much does the answer change if you are wrong by one percentage point?
- The inheritance clause pays a deceased winner's heirs only for what remains of 20 years from the claim date. How would you expect that clause to change the value of the annuity compared with a version that had no such floor?
- Suppose you were 65 rather than 20 when you won. How would a shorter expected collection horizon change the comparison between the lump sum and the weekly payments, and which of the two choices would you expect to look more attractive?
Sources
- Loto-Quebec, "Gagnant a vie" official game rules, assets.lotoquebec.com. assets.lotoquebec.com. Primary source for ticket cost, prize structure, odds and the annuity/inheritance rules.
- Loto-Quebec, press release, "Gagnant Aubin-Vega, Gagnant a vie", 3 July 2025. societe.lotoquebec.com. Primary source for the winner's name, city, purchase location, retailer commission and the 2025 lifetime-annuity winner count.
- CTV News Montreal, "Montreal woman wins $1,000 a week for life", 4 July 2025. ctvnews.ca. Independent press corroboration of the win.
- Yahoo News Canada, "20-year-old lottery winner decides against $1M lump sum, opts for lifetime weekly annuity in hopes of buying a home", 15 September 2025. ca.news.yahoo.com. Source for the reported age of 20 and for press commentary on the simple annual-yield framing.
- Mind Your Decisions, "Lottery Winner Rejects $1 Million For $1000 Weekly Payments For Life", 17 December 2025. mindyourdecisions.com. Independent present-value analysis using 5% and 8% discount-rate scenarios, corroborating a breakeven close to 5%.
