$4)$ Sue Gorsh established a savings account for her son's college education by making annual deposits of $$10,000$ at the beginning of each of six years to a savings account paying $8\%.$ At the end of the sixth year, the account balance was transferred to a bank paying $10\%,$ and annual deposits of $$10,000$ were made at the end of each year from the seventh through the tenth years. What was the account balance at the end of the tenth year?