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

Child Tax Credit Allowed
a. A single parent with modified AGI of $213,400 and one child age 4.
b. A single parent with modified AGI of $78,000 and three children ages 7, 9, and 12.
c. A married couple, filing jointly, with modified AGI of $407,933 and two children age 14 and 16.
d. A married couple, filing jointly, with modified AGI of $132,055 and one child, age 13.