Will and Joan, cash basis taxpayers, timely filed their joint federal income tax return for the year $20$x$7$ on August $1,20$x$8,$ after having been granted an extension of time to file until October $15,20$x$8.$ The tax liability shown on the return was $$150,000.$ A total of $$35,000$ had been paid by withholding from their salaries and $$40,000$ had been paid in four equal installments of estimated tax in the amount of $$10,000$ each. The balance of $$75,000$ was paid at the time the return was filed.

The $20$x$7$ tax return was selected by the IRS for examination in June $20$x$9.$ At the end of the examination, the IRS proposed a deficiency in tax in the amount of $$80,000.$ Will and Joan asked their lawyer to file a protest with the IRS on their behalf and to request a conference with an Appeals Officer. Unfortunately, however, the Appeals Officer agreed with the proposed deficiency, Will and Joan were not willing to agree, and the Appeals Officer issued a statutory notice of deficiency in the amount of $$80,000$ for the year.

Will and Joan felt strongly about their case and asked their lawyer to file a petition to the Tax Court for the year. After trial, the Court agreed with Will and Joan as to $$30,000$ of the deficiency but sustained the IRS$$ determination as to the remaining $$50,000.$ No appeals were filed, and the decision of the Tax Court became final on November $1,20$X$0.$Soon thereafter, Will and Joan received a notice from the IRS, dated November $15,20$x$0,$ demanding payment of $$50,000,$ plus interest, for the year $20$x$7.$

$1.$ What payments are subject to interest? How is the interest calculated?

$2.$ How long do Will and Joan have to pay the $$50,000$ deficiency? What would be the result if it was not paid in time?

$3.$ Assume for this Part $3$ that settlement discussions with the IRS Appeals Office before the statutory notice of deficiency was issued was successful. Will and Joan executed the appropriate Form $870$ on July $1,20$x$9.$ The IRS sent them a notice and demand dated December $15,20$x$9$ for the payment of the agreed amount of tax. What are the relevant dates for calculating the interest on the amount due?Soon thereafter, Will and Joan received a notice from the IRS, dated November $15,20$x$0,$ demanding payment of $$50,000,$ plus interest, for the year $20$x$7.$

$1.$ What payments are subject to interest? How is the interest calculated?

$2.$ How long do Will and Joan have to pay the $$50,000$ deficiency? What would be the result if it was not paid in time?

$3.$ Assume for this Part $3$ that settlement discussions with the IRS Appeals Office before the statutory notice of deficiency was issued was successful. Will and Joan executed the appropriate Form $870$ on July $1,20$x$9.$ The IRS sent them a notice and demand dated December $15,20$x$9$ for the payment of the agreed amount of tax. What are the relevant dates for calculating the interest on the amount due?