Cook Security Systems has a $$37,500$ line of credit, which charges an annual percentage rate of prime rate plus $4\%.$ The starting balance on October $1$ was $$9,700.$

On October $4$ they made a payment of $$1,400.$ On October $13$ the business borrowed $$2,500,$ and on October $19$ they borrowed $$4,400.$ If the current prime rate is $8\%,$ what is the new balance $($in $$)?($Round your answer to the nearest cent.$)$