A construction contractor borrows $$50,000$ to take advantage of a $2\%$ cash discount offered on material required for the project. The note is a single note payable in $60$ days at an $11\%$ annual interest rate $($assumed $365$ days$).$ However, the contractor receives construction progress payments and applies part of the note as follows:

A$.$ $$20,000$ paid on the note $15$ days after the note is made.

B$.$ $$20,000$ paid $30$ days from the date of the original note.

C$.$ $$10,000$ balance paid on the maturity date of $60$ days.

Assumption: With simple interest, single payment notes, any amount paid on the principal stops the interest paid on that amount as of the date payment is made.

Find the total amount of interest paid, how much money the contractor saved by making partial payments on the note, and the percent saved.