You are the vice president of finance for Neptune Enterprises. Inc., a manufacturer of scuba diving gear. The company is planning a major plant expansion in $5$ years. You have decided to start a sinking fund to accumulate the funds necessary for the project. Your company's investments yield $8\%$ compounded quarterly. It is estimated that $$2,000,000$ in today's dollars will be required; however, the inflation rate on construction costs and plant equipment is expected to average $5\%$ per year for the next $5$ years.

a$.$ Use the compound interest concept from Chapter $11$ to determine how much will be required for the project, taking inflation into account.

b$.$ What sinking fund payments will be required at the end of every $3-$month period to accumulate the necessary funds?