First, you’re reading the qualifications wrong.
For your own legal child under age 24 (biological, step, or adopted) they must live more than half the year in your home and not provide more than 50% of their own support, and be a full time student.
Most of the time, being away at school is considered a temporary absence and the child is considered to live “at home.” This seems particularly true in your case if the child returns home for summer, and if it is likely that they would return home after graduation, and they still keep stuff at your house. They would only be considered to have moved out if they have made a permanent move away from your home, such as they have moved into an apartment with a romantic partner, or gotten married, or taken some other step which definitively makes them no longer part of your household.
Now as to the question of “did the child provide more than half of their own support“, support is all the money that is spent to provide for the child‘s living expenses. Money spent on support includes money spent for tuition, rent, food, clothing, travel, entertainment, and medical costs. Money spent on support does not count assets in the bank, nor does it count support spent for other people. For example, if the child has $100,000 in an investment account and withdraws $5000 to pay their own rent and $10,000 to pay for the food, clothing, and other expenses of their live-in romantic partner who does not have a job, then the child has only spent $5000 on their own support, regardless of money spent on other people’s support or money in the bank.
Scholarships and grants do not count as support paid by anyone, for purposes of this calculation. Tuition paid for by a loan in the student’s name is considered support that the student pays for themself, since they are obligated to repay the loan, while tuition paid for by a parent or parent loan counts as support paid for by the parent.
A gift to the child counts as support if the child uses it for living expenses but does not count as support if the child puts it in their IRA for retirement or uses it for something other than their own living expenses.
You include the value of room and board that you provide to your child as expenses that you pay for, using a prorated share of your mortgage, food, hazard insurance, utilities, and other household expenses based on the number of people living in the home.
I hope you can see where this is all going.
Because of the high cost of college, and the general low income of most college students, it is much more common for a child student to be a dependent, and it is uncommon for the child to pay more than half their own expenses so as to not be a tax dependent.
From your math, the child has $50,000 of expenses “on their own” plus another $5000 or so that you provide indirectly. Your child spends $17,000 of their own income on their support. The value of the investment fund is irrelevant unless the child withdraws money from the investment account to pay their living expenses. I don’t see any other money from the child going toward the child‘s expenses. So it seems as though the child does not pay more than 50% of their own support.
However, you may want to re-analyze the situation using the principles I outlined above.
