Noah has always dreamed of having a yacht. When he was $18,$ he decided to start saving money to buy one. He learned that the cost of a yacht starts at $5500\mathrm{.}000.$a$.$ If his goal is to own a yacht by age $30,$ how much should he deposit each quarter into an account with an APR of $8\mathrm{.}7\%$ in order to have enough money to purchase a $$500,000$ yacht? Round your answer to the nearest dollar.b$.$ If he reaches his goal, how much of the $$500,000,$ will come from deposits, and how much will come from interest?