Show me the steps to solve Joe was employed by Liberal Arts College on a $10\mathrm{.}5-$month contract that called for him to be paid a total of $$100,000$ in $21$ semi$-$monthly installments $($in arrears$).$ The day before he was to receive his first payment, he was informed that he would now be paid in $20$ installments equal to one twenty$-$fourth of his salary followed by a final payment equal to one sixth of his salary. Joe had made financial commitments expecting he would be paid according to the terms of his contract with Liberal Arts College. To satisfy those commitments, he had to borrow the difference using his credit card at an annual rate of $28\%$ annually compounded monthly. What did Liberal Arts College's actions cost Joe over the tenor of his contract?