For a $25-$year loan of $12,000$ at $6\%$ nominal annual interest $($compounded semiannually$)$

with payments at the end of each half year find the following:

$($a$)$ The semiannual payment amount $[466\mathrm{.}39]$

$($b$)$ The outstanding balance after the $20$th payment $[9,141\mathrm{.}26]$

$($c$)$ The amount of interest in the $20$th payment $[279\mathrm{.}83]$

$($d$)$ The amount of principal in the $20$th payment $[186\mathrm{.}56]$

$($e$)$ The amount of interest in the $30$th payment $[215\mathrm{.}67]$

CORRECT ANSWERS ARE GIVEN IN PARENTHESIS