Julie, being self-employed, is required to make estimated payments of her tax liability for the year. Her tax liability for 2016 was $25,000, and her AGI was less than $150,000. For 2017, Julie ultimately determines that her income tax liability is $18,000. During the year, however, she made the following payments, totaling $13,000:

April 18, 2017	$4,500
June 15, 2017	2,800
September 15, 2017	4,100
January 16, 2018	1,600
Total paid	$13,000

Because Julie prepaid so little of her ultimate income tax liability, she now realizes that she may be subject to the penalty for underpayment of estimated tax.

a. Based on this information, Julie's required annual payment for estimated taxes should have been $, and each quarterly installment would have been $.

b. The amount by which Julie underpaid her estimated tax is $.

c. If Julie's tax liability for 2016 was $15,960, then the amount by which she underpaid her estimated taxes is $.