On April $1$st$,$ Bob the Builder entered into a contract of one$-$month duration to build a barn for Nolan. Bob is guaranteed to receive a base fee of $$6,000$ for his services in addition to a bonus depending on when the project is completed. Nolan created incentives for Bob to finish the barn as soon as he can without jeopardizing the structural integrity of the barn. Nolan offered to pay an additional $20\%$ of the base fee if the project finished $2$ weeks early and $15\%$ if the project finished a week early. The probability of finishing $2$ weeks early is $20\%$ and the probability of finishing a week early is $65\%.$