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

a. A single parent with a modified AGI of $214,100 and one child age 4.

b. A single parent with a modified AGI of $78,700 and three children ages 7, 9, and 12.

c. A married couple, filing jointly, with a modified AGI of $408,633 and two children aged 14 and 16.

d. A married couple, filing jointly, with a modified AGI of $132,755 and one child, age 13.