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Suppose that you take out a loan for $$100,000.$ The loan has a term of $30$ years,

with monthly payments. The nominal annual interest rate is $8\%.$ Please determine

the following: $($a$)$ actual amount of monthly payment; $($b$)$ outstanding balance on

loan after $5$ years; $($c$)$ amount of principal paid during first $5$ years combined;

$($d$)$ amount of interest paid during first $5$ years combined; $($e$)$ amount of principal

paid during the $5$th year specifically; $($f$)$ amount of interest paid during the $5$th year

specifically