Sharon Fox decided to buy a home in Marblehead, Massachusetts, for $$273,000.$ Her bank requires a $30\%$ down payment. Sue Willis, an attorney, has notified Sharon that besides the $30\%$ down payment there will be the following additional costs:

Recording of the deed $ $28\mathrm{.}00$

A credit and appraisal report $153\mathrm{.}00$

Preparation of appropriate documents $46\mathrm{.}00$

In addition, there will be a transfer tax of $1\mathrm{.}8\%$ of the purchase price and a loan origination fee of $2\mathrm{.}5\%$ of the mortgage amount. Assume a $30-$year mortgage at a rate of $10\%.$

a$.$ What is the initial amount of cash Sharon will need? $($Do not round intermediate calculations. Round your answer to the nearest cent.$)$

b$.$ What is her monthly payment? $($Do not round intermediate calculations. Round your answer to the nearest cent.$)$

c$.$ What is the total cost of interest over the life of the mortgage? $($Do not round intermediate calculations. Round your answer to the nearest cent.$)$