A lottery offers two options for the prize. Option A: $1000 a week for life. Option B: $600 000 in one lump sum.?

i would rather have the first one

1000 * 52 * k = 600000 * (1 + 0.03/12)^(12k)

52000 * k = 600000 * (1 + 0.0025)^(12k)

52 * k = 600 * 1.0025^(12k)

13 * k = 150 * 1.0025^(12k)

https://www.wolframalpha.com/input/?i=13+*+k+%3D+1...

For the first 23 years, roughly, taking the 600,000 lump sum and investing it results in a greater total than what you would have gotten if you took 1,000 per week. From 23 years to about 46.5 years, the $1,000 per week will yield more and after 46.5 years, the original plan works out better.

That's assuming, of course, that you don't spend any of it.

Now, if you were spending money over the next 50 years, you'd want to set up periodic withdrawals that will zero out at the 50 year mark. Let's assume that you'll drop dead after 50 years and that there are 52 payments per year

1000 * 52 * 50 =>

1000 * 100 * 26 =>

2,600,000

That's what you'd get after 50 years of $1,000 per week.

Now, we're going to say that you're going to get 50 * 12, or 600 equal monthly payments over the course of that 50 years.

((((((....(((600000 * 1.0025 - P) * 1.0025 - P) * 1.0025 - P) * .....) * 1.0025 - P = 0

If we solve for the 600000, we get this:

600000 = P/1.0025 + P/1.0025^2 + P/1.0025^3 + .... + P/1.0025^600

We can rewrite this geometric sum and solve for P

600000 = P * (1/1.0025 + 1/1.0025^2 + ... + 1/1.0025^600)

S = 1/1.0025 + 1/1.0025^2 + ... + 1/1.0025^600

S = r + r^2 + r^3 + ... + r^600

Sr = r^2 + r^3 + r^4 + ... + r^601

Sr - S = r^2 + r^3 + r^4 + ... + r^601 - (r + r^2 + r^3 + ... + r^600)

S * (r - 1) = r^(601) + r^(600) - r^(600) + ... + r^3 - r^3 + r^2 - r^2 - r

S * (r - 1) = r^(601) - r

S = r * (r^(600) - 1) / (r - 1)

S = r * (1 - r^(600)) / (1 - r)

S = (1/1.0025) * (1 - (1/1.0025)^600) / (1 - 1/1.0025)

S = 1 * (1 - 1.0025^(-600)) / (1.0025 - 1)

S = (1 - 1.0025^(-600)) / 0.0025

S = (1 - 1.0025^(-600)) / (25/10000)

S = (1 - 1.0025^(-600)) / (1/400)

S = 400 * (1 - 1.0025^(-600)) / 1

S = 400 * (1 - 1.0025^(-600))

600000 = P * (1/1.0025 + 1/1.0025^2 + ... + 1/1.0025^600)

600000 = P * S

600000 = P * 400 * (1 - 1.0025^(-600))

1500 = P * (1 - 1.0025^(-600))

1500 / (1 - 1.0025^(-600)) = P

P = ‭1,931.8649877615876302071469910772‬

So, you'll get 600 monthly payments of 1931.86, for a total of ‭1,159,116‬.

Either way, I would take the $1,000 each week for life. Sure, after 46.5 years, you'll have more money, if you never touch your money, but what's the point of that? A lot can happen in 50 years. I'd take Option A, either way.

If this is a math question about the higher number that is one thing...

If this is an abstract about what would be the more uplifting decision the answer is totally subjective.

For me I would choose the lump sum whether it is more or less, since you never know whether or not the lottery might go bankrupt.

That's me, anyway.

Usually there's a guaranteed payout amount, because of that, I would take the $1000 per week for life - even if you die young, they have to pay a certain amount to your estate.

Having said that, collecting $52K for 50 years is $2.6 Million. $52K added to my projected retirement income would be pretty sweet. Also, if I won that I would bank the money for at least a year or two before I started using any of it.

Take the 600,000 and if you invest it all, you will make 2.6 million in 50 years which is the same amount you'd receive in total if you chose the other option, that is if you do in fact live another 50 years, that's not a guarantee, so take the money you can get and invest

If you invest all of the $600,000, then Option A is not better at any point in time.

If not, that's a lot of math to calculate that I'm not going to do.

the first one sounds better