# Thread: Minimum days until expected values reach $1,000,000? 1. ## Minimum days until expected values reach$1,000,000?

Given the left page scenario, what is the minimum number of days until the expected value rebalances to \$1,000,000?
The diagram on the right demonstrates pictorially how expected values are calculated per day iteration

2. Awesome problem. There is much to consider, here. Why don't you share with us some of what you have considered?

Thought Question: with a .5 + .25 * 2 + .25 * (1/2) = .5 + .5 + .125 = 1.125 daily expected portfolio growth, are we SURE to get anywhere?

3. Originally Posted by tkhunny
Awesome problem. There is much to consider, here. Why don't you share with us some of what you have considered?

Thought Question: with a .5 + .25 * 2 + .25 * (1/2) = .5 + .5 + .125 = 1.125 daily expected portfolio growth, are we SURE to get anywhere?
Hey! I believe I have solved it. I calculated the expected values at the first three consecutive days, and derived a sequence formula for the nth expected value. Then I set it equal to 1,000,000 and voila! I got around n≈117.29 which rounds up to 118 days.

Confirmation or flat-out rejection of my proposed solution would be appreciated

4. Well, okay, but why did we do that? It's a consistent, well-defined, recursive process.

$1.125^{n} = 1,000,000 \implies n = 117.2962683$

Did we need to draw the tree?

5. Originally Posted by tkhunny
Well, okay, but why did we do that? It's a consistent, well-defined, recursive process.

$1.125^{n} = 1,000,000\implies n = 117.2962683$

Did we need to draw the tree?
Wow, stumped. That's amazing... I need to study more.

6. Originally Posted by nigahiga
Wow, stumped. That's amazing... I need to study more.
Keep up the good work. Remember my signature.

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