$(20$ points$)$ A home improvement store is offering the following two payment options for a new luxury

kitchen appliance bundle that costs $$12,600.$ You can pay cash now or you can choose the store's installment

offer $-$ equal payments payable at the end of each month starting one month from now over a $2-$year period at

$0\%$ interest rate for a small monthly processing fee of $$50$ that needs to be paid along with each monthly

payment. I claim that you will end up paying an effective annual rate of approximately $9\mathrm{.}38\%$ if you choose

the installment offer. Do you agree with me$?$ Show work to support your answer.