Tyler invested $$20,300$ in a mutual fund at $2\mathrm{.}8\%$ compounded semi$-$annually. After $3$ years, the interest rate was changed to $8\mathrm{.}2\%$ compounded annually. After the rate change, the money is left in the account for an additional $8$ years.

How much was the value of the fund after the full $11$ years?