Calculating Late Filing/Paying Penalties

Course: Income Tax Planning
Lesson 1: Introduction to Taxation
Student Question:
For this question, could you send me the math behind finding the answer? I want a better understanding of how the penalty was assessed.
Review Exercise:
Jerry’s taxes were due April 15th. He filed his return in October of the same year and paid his $3,000 two months later (on December 30th). Would Jerry be subject to a penalty? How much?
Thanks,
Andrew
Instructor Response:
Hi Andrew,
Failure to File:
You are correct. Whenever the failure to file penalty and the failure to pay penalty run concurrently, the failure to file penalty is reduced to 4.5%/month. The maximum number of months that the failure to file penalty may be assessed is generally 5 months. In this case, the five months are the months ending May 15, June 15, July 15, August 15, and September 15.
5 months x 4.5% per month = $675
Failure to Pay:
The failure to file penalty remains at .5% when the failure to pay and failure to file penalties run concurrently. Penalties are assessed for each full month or fraction thereof.
May 15 through December 15 = 8 penalty months
December 16 through December 30 = 1 penalty month
9 months x .5% per month = $135
Total penalty and interest = $810
Onward and Upward,
Bruce