Suppose you have an opportunity to invest in a fund that pays $13\%$ interest compounded annually.$$ Today, you invest

$$$$5$ comma $000$ into this fund. Three years later$($EOY $3),$ you borrow $$$$2$ comma $500$ from a local bank at $8\%$ annual interest and invest it in the fund. Two years later$($EOY $5),$ you withdraw enough money from the fund to repay the bank loan and all interest due on it$.$ Three years from this withdrawal$($EOY $8)$ you start taking $$$$1$ comma $000$ per year out of the fund. After five withdrawals of $$$$1$ comma $000,$ you have withdrawn your original $$$$5$ comma $000.$ The amount remaining in the fund is earned interest. How much$$ remains?