MS$.$ BROWN SIGNED AN $$8,400$ NOTE WITH INTEREST AT $8\%$ ON JANUARY $4.$ THE NOTE IS DUE ON DECEMBER $1.$ SHE PAID BACK $$3,000$ ON JUNE $1.$ IF THE PAYMENT WAS FIRST APPLIED TO INTEREST AND THEN PRINCIPAL, HOW MUCH WILL MS$.$ BROWN OWE AT THE END OF THE YEAR?

a$)$ $$8,400$

b$)$ $$6,009\mathrm{.}40$

c$)$ $$9,009\mathrm{.}40$

d$)$ $$5,907\mathrm{.}10$

e$),$$$478\mathrm{.}14$