Sarah is a $30-$year$-$old software engineer. Right after Sarah graduated from college, she was able to land a stable job, and purchased her first home five years ago. At the time, she put down $20\%$ as a down payment and financed the rest through a mortgage to purchase a charming house listed for $$400,000.$

$($a$)$ Suppose she got a five$-$year term, fixed, closed mortgage, with amortization period of $25$ years and $3\%$ APR. How much does she still owe after five years of payments?

$($b$)$ How much interest did she repay in the first five years?

$($c$)$ If she wants to sell the property today, what would the net proceeds be$?$ Assume that all costs associated with the sale are $$18,000$ and home values increased at $3\%$ annually for the past five years.

$($d$)$ If she opt not to sell but renew their mortgage at a rate of $6\%$ with current mortgagee, what would be the new monthly payment amount?

$($e$)$ Sarah asked your advice on whether to sell the property $($part c$)$ or renew the mortgage $($part d$).$ However, you simply do not have enough information to make a recommendation right now. Demonstrate at least $(1)$ two financial factors and $(2)$ two non$-$financial factors you should consider when making the suggestion.