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Your brother is a half owner of the house as of today, so today's value is used. However, you would be entitled to reimbursement for 50% of the taxes, insurance, maintenance, etc. It's possible that you could also be reimbursed for part of the $20k improvements, although he can argue that they weren't necessary, that you didn't get his consent, and that you improved the property at your own risk and expense. So that last issue could go either way.
Does that answer your question? Please let me know if you need clarification, as I am happy to continue helping you until you are satisfied.
He does have the argument that the statute of limitations applies and that you cannot collect for many of those years. But that only applies if you were to sue him. If he wants to make a deal, then you can demand that he pay half. Also, it's not certain that you can't collect all the way back to 2006 if this ends up in court. For example, a partition suit is equitable in nature, and a judge may not have to pay attention to the statute of limitations in that type of case.
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