Given Principal: $$13,500,9\%,240$ days

Partial payments: On $100$th day, $$3,800$

On $180$th day, $$2,500$

a$.$ Use the U$.$S$.$ Rule to solve for total interest cost. $($Use $360$ days a year. Do not round intermediate calculations. Round your answer to the nearest cent.$)$

b$.$ Use the U$.$S$.$ Rule to solve for principal balances. $($Use $360$ days a year. Do not round intermediate calculations. Round your answers to the nearest cent.$)$

c$.$ Use the U$.$S$.$ Rule to solve for final payment. $($Use $360$ days a year. Do not round intermediate calculations. Round your answer to the nearest cent.$)$