Sharon Fox decided to buy a home in Marblehead, Massachusetts, for $282,000. Her bank requires a 20% down payment. Sue Willis, an attorney, has notified Sharon that besides the 20% down payment there will be the following additional costs: In addition, there will be a transfer tax of 2% of the purchase price and a loan origination fee of 2% of the mortgage amount. Assume a 30 -year mortgage at a rate of 10.5%. a. What is the initial amount of cash Sharon will need? (Do not round intermediate calculations. Round your answer to the nearest cent.)