Made the smart choice there, $52,000 a year is nothing to balk at even after taxes.
I love how there are so many comments that I found that are trying to imply that she is dumb for doing this. Or that our generation is stupid. But...shes 20!
Assuming that she lives to be 80, that is $3.12 million. Over triple the amount offered to begin with. All the while paying less in taxes because it is in a SIGNIFICANTLY lower tax bracket as a passive income rather than a lump sum. (Assuming this is in the US. The article I found was in Canada and they do not tax lottery income.)
So, while the goal may be to make her sound stupid, for doing this. It sounds to me like SHE is the only one who paid attention in math!
That's a pretty unfair comparison, you're only considering the time value of money for one of the two options but not the other.
That million is not (or at least shouldn't be) sitting in a bank account. It should be properly invested and out there gathering interest. And that's where the math gets more complicated, the annuity gets more input capital over time and gets interest on the existing capital, but the lump sum starts gathering interest on the full million immediately. There's therefore a chance that the annuity could "catch up" to the lump sum, or that the lump sum is simply growing too fast to catch up.
Thankfully, as it turns out, there's an easy way to go about it: If the lump sum gets more interest per year than the annuity, then the annuity can never catch up. (Rearranging the terms, it's the same as saying that the ratio of annuity to lump sum must be bigger than the expected interest rate). That's because, for every dollar you get in annuity, the lump sum will get more than a dollar in interest, so the difference between the two can only grow. The same argument reversed proves that the annuity will catch up if it's higher than the interest. It might take a long time (34 years for a 70k annuity at 6% interest), but it will happen.
In this case, I'm not sure enough about US taxes to say (and there's an argument to be made that the money is taxed at her marginal tax bracket if it's added to her income, making the rate steeper), but assuming untaxed or post-tax for both, the number to beat is 5.2%. Depending on your guess of how the next 40 years are going to go, that is either easily beatable (historical returns for broad US ETFs being in the 7-12% range) or impossible (asset meltdown hypothesis). That's where the nuance is.
Safety is another argument that sounds overwhelmingly in favor of the annuity, but where the truth is also more nuanced. You can lose the lump sum, while the annuity is paid for life... or until the lottery company goes out of business. The lump sum is yours, and only you have the ability to lose it. And if you think the lottery company isn't going out of business during your lifetime, then what's preventing you from investing part of the lump sum into it as a sure option?
The only argument that I think is 100% in favor of the annuity is psychological. A lump sum is tempting, it allows you to do bad financial decisions like buy a house or a cool new car, which even in small doses can make your interest plummet. Spend just 10% on yourself and now your 6% interest is only 54k a year, barely enough to win over the annuity. In contrast, you can be completely financially irresponsible with the annuity and lose it all on red, and it's back the next year. If the lump sum is better in a particular situation, that's only with the discipline to not spend it until it reaches the amount you set your sights on. And considering the statistics on credit card debt, a good amount of Americans most likely don't have that discipline. In contrast, the annuity can be completely lost at the casino one year, and back the next, no discipline required.
So yeah, the annuity may have been good in her case, but it's not always going to be the best, it's a lot more nuanced than just "after 60 years that's 3x more than the million"
