Determine the amount of the child tax credit in each of the following cases:

$\backslash$table$[[,\backslash$table$[[$Child Tax$],[$Credit$],[$Allowed$]]],[$a$.$ A single parent with modified AGI of $$214,600$ and one child age $4.,],[$b$.$ A single parent with modified AGI of $$79,200$ and three children ages $7,9,$ and $12.,],[$c$.$ A married couple, filing jointly, with modified AGI of $$409,133$ and two children age $14$ and $16,],[$d$.$ A married couple, filing jointly, with modified AGI of $$133,255$ and one child, age $13.,]]$