On April 13, 2022, Amanda, a calendar year taxpayer, sat down to prepare her 2021 tax return. Realizing that she did not have time to get it done, she decided to file for an extension. Amandas tax liability for the previous year, 2020, was $8,000. During 2021 Amandas employer withheld $2,500 and Amanda paid estimated taxes of $500. Amanda estimates that her final gross tax liability for 2021 will be $12,000.

a. What amount must Amanda pay by April 15 to avoid a failure-to-pay penalty?

b. Amanda completed and filed her return on July 20, 2022. Unfortunately, her initial estimate of her tax was low and her final tax (before withholding and estimated tax payments) was $15,000. Assuming Amanda paid the amount determined in (a) above, what is the amount of the failure-to-pay penalty, if any?