A homebuilder has taken out a $$200,000$ loan with $6\%$ APR with quarterly compounding to build a house.

On this loan, the firm is supposed to pay an equal amount every quarter for the next two years. The first

payment will be a quarter from now.

$($a$)$ What will the quarterly payment be$?$

$($b$)$ Present the amortization schedule as below:

Quarter Beginning balance Total payment Interest paid P