Sharon Fox decided to buy a home in Marblehead, Massachusetts, for $$278,000.$ 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:

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.$)$

Initial amount

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

Monthly payment

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.$)$

Total cost of interest