A student needs to borrow $$8,000$ to pay for college. She can get the loan at an APR of $10\mathrm{.}75\%$ to be paid off in monthly installments over the next $4$ years.

If she decides to pay the loan off in monthly installments over $3$ years instead of $4$ years at the given APR, how much money will she save altogether? Round your answer to the nearest cent.$)$