Consider the below cash$-$flow diagram.

$($a$)$ If A $=$ $$200,$ i$\%=12\%$ per year, and N $=5$ years, then P $=?(4$ points$)$

$($b$)$ If P $=$ $$1,000,$ i$\%=12\%$ per year, and N $=5$ years, then A $=?(4$ points$)$

$($c$)$ If P $=$ $$1,000,$ A $=$ $$200,$ and i$\%=12\%$ per year, then N $=?(6$ points$)$

$($d$)$ If P $=$ $$1,000,$ A $=$ $$200,$ and N $=10$ years, then i $=?(6$ points$)$