$4.$ IBM sold a mainframe computer to its customer for $60$ monthly payments of $$92,082\mathrm{.}61,$ which totals $$5,524,956\mathrm{.}60.$ IBM also agreed to provide installation and training for the customer for no additional charges. According to the agreement the customer is not required to use IBM for installation and training. IBM estimated that the standalone installation and training sales prices are $$50,000$ and $$68,000,$ respectively. IBM used a $4\%$ annual interest rate in determining the $60$ monthly payments. The customer decided to have IBM install and train its employees and IBM delivered the computer on July $1$ and completed installation on October $31.$ Training will take place over the next $12$ months. The date of delivery starts the customer's payment obligation to IBM and IBM's year end is December $31.$

A$.$ What date may IBM recognize revenue from this transaction $[1$ point$]$

B$.$ What is the total revenue amount and the related revenue component amounts IBM may recognize on the date specified in answer A$?[$You must show your work for credit.$][7$ points$]$

C$.$ How much interest income $($revenue$)$ will IBM recognize in its December $31$ regular income statement from this transaction? $[$Hint: Set up the amortization schedule of the sales price. You must show your work for credit.$][2(1)/(2)$ points$]$