Sharon Fox decided to buy a home in Marblehead, Massachusetts, for $$275,000.$ 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: $($Use Table $15\mathrm{.}1)$

Recording of the deed

A credit and appraisal report

$$30\mathrm{.}00$

Preparation of appropriate documents

$155\mathrm{.}00$

$48\mathrm{.}00$

Other closing expenses include 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 $20-$year mortgage at a rate of $3\frac{5}{8}\%.$

a$.$ What is the initial amount of cash Sharon will need?

Note: Do not round intermediate calculations. Round your answer to the nearest cent.

Initial amount of cash needed

b$.$ What is her monthly payment?

Note: Do not round intermediate calculations. Round your answer to the nearest cent.

Monthly payment