Lily borrows USD$200,000$ for $30$ years at $6\%$ annually. She agrees to make

annual payments of USD$12,000$ for the first $10$ years, and USD$12,000+P$ for

the next $20$ years. By answering the following questions correct to two

decimal places,

a$.$ Find $P.$

b$.$ Find the outstanding loan balance at the end of $5$ years.

c$.$ Find the outstanding loan balance at the end of $20$ years.

d$.$ Find the total of interest amount paid of the loan over $30$ years.