Sarah is going to borrow money for her college expenses. Her local credit union will lend Sarah $$$$10000$ now at a nominal interest rate of $4\%$ per$$ year, compounded quarterly. Then after two $$years$,$ the credit union will lend her an additional $$$$10000$ at a higher interest rate of $10\%$ per year compounded annually. Sarah will repay these loans over four years when she graduates. How much does Sarah owe the credit union when she graduates $4$ years after starting$$ college?