(b) Other installments.--In privilege periods of twelve months ending at any time during the calendar year nineteen hundred seventy and thereafter, the estimated tax or estimated tax surcharge, with respect to which a declaration for such privilege period is required shall be paid, in the case of a taxpayer which reports on the basis of a calendar year, as follows:

(1) If the declaration is filed on or before June fifteenth, the estimated tax or estimated tax surcharge shown thereon, after applying thereto the amount, if any, paid during the same privilege period pursuant to subdivision (a), shall be paid in three equal installments. One of such installments shall be paid at the time of the filing of the declaration, one shall be paid on the following September fifteenth, and one on the following December fifteenth.

(2) If the declaration is filed after June fifteenth and not after September fifteenth of such privilege period, and is not required to be filed on or before June fifteenth of such period, the estimated tax or estimated tax surcharge shown on such declaration, after applying thereto the amount, if any, paid during the same privilege period pursuant to subdivision (a), shall be paid in two equal installments. One of such installments shall be paid at the time of the filing of the declaration and one shall be paid on the following December fifteenth.

(3) If the declaration is filed after September fifteenth of such privilege period, and is not required to be filed on or before September fifteenth of such privilege period, the estimated tax or estimated tax surcharge shown on such declaration, after applying thereto the amount, if any, paid in respect of such privilege period pursuant to subdivision (a), shall be paid in full at the time of the filing of the declaration.

(4) If the declaration is filed after the time prescribed therefor, or after the expiration of any extension of time therefor, paragraphs (2) and (3) of this subdivision shall not apply, and there shall be paid at the time of such filing all installments of estimated tax or estimated tax surcharge payable at or before such time, and the remaining installments shall be paid at the times at which, and in the amounts in which, they would have been payable if the declaration had been filed when due.

(c) Amendments of declaration.--If any amendment of a declaration is filed, the remaining installments, if any, shall be ratably increased or decreased (as the case may be) to reflect any increase or decrease in the estimated tax or estimated tax surcharge by reason of such amendment, and if any amendment is made after September fifteenth of the privilege period, any increase in the estimated tax or estimated tax surcharge by reason thereof shall be paid at the time of making such amendment.

(d) Application of installments based on the second preceding year's tax.--(1) Any amount paid pursuant to subdivision (a) shall be applied after payment as a first installment against the estimated tax or estimated tax surcharge, respectively, of the taxpayer for the current privilege period shown on the declaration required to be filed pursuant to section two hundred thirteen-a of this chapter or, if no declaration of estimated tax or a declaration of estimated tax surcharge is required to be filed by the taxpayer pursuant to such section, any such amount shall be considered a payment on account of the tax or tax surcharge shown on the report required to be filed by the taxpayer for such privilege period.

(2) Any amount paid pursuant to paragraph four of subsection (c) of section six hundred fifty-eight of this chapter on behalf of a taxpayer subject to tax under this article shall be applied against the estimated tax of the taxpayer for the taxable year shown on the declaration required to be filed pursuant to section two hundred thirteen-a of this article, or if no declaration is filed pursuant to such section, any such amount shall be considered a payment on account of the tax on the return required to be filed by the taxpayer for such taxable year.

(e) Interest on certain installments based on the second preceding year's tax.--Notwithstanding the provisions of section one thousand eighty-eight of this chapter or of section sixteen of the state finance law, if an amount paid pursuant to subdivision (a) exceeds the tax or tax surcharge, respectively, shown on the report required to be filed by the taxpayer for the privilege period during which the amount was paid, interest shall be allowed and paid on the amount by which the amount so paid pursuant to such subdivision exceeds such tax or tax surcharge. In the case of amounts so paid pursuant to subdivision (a), such interest shall be allowed and paid at the overpayment rate set by the commissioner of taxation and finance pursuant to section one thousand ninety-six of this chapter, or if no rate is set, at the rate of six per centum per annum from the date of payment of the amount so paid pursuant to such subdivision to the fifteenth day of the fourth month following the close of the taxable year, provided, however, that no interest shall be allowed or paid under this subdivision if the amount thereof is less than one dollar or if such interest becomes payable solely because of a carryback of a net operating loss in a subsequent privilege period.

(f) The preceding year's tax and the second preceding year's tax defined.-- As used in this section, "the preceding year's tax" means the tax imposed upon the taxpayer by section two hundred nine of this article for the preceding calendar or fiscal year, or, for purposes of computing the first installment of estimated tax when an application has been filed for extension of the time for filing the report required to be filed for such preceding calendar or fiscal year, the amount properly estimated pursuant to section two hundred thirteen of this article as the tax imposed upon the taxpayer for such calendar or fiscal year. As used in this section, "the second preceding year's tax" means the tax imposed upon the taxpayer by section two hundred nine of this article for the second preceding calendar or fiscal year.

(g) Application to short privilege period.--This section shall apply to a privilege period of less than twelve months in accordance with regulations of the tax commission.

(h) Fiscal year.--The provisions of this section shall apply to privilege periods of twelve months other than a calendar year by the substitution of the months of such fiscal year for the corresponding months specified in such provisions.

(i) Extension of time.--The commissioner of taxation and finance may grant a reasonable extension of time, not to exceed six months, for payment of any installment of estimated tax or estimated tax surcharge required pursuant to this section, on such terms and conditions as he may require, including the furnishing of a bond or other security by the taxpayer in an amount not exceeding twice the amount for which any extension of time for payment is granted, provided however that interest at the underpayment rate set by the commissioner pursuant to section one thousand ninety-six of this chapter, or if no rate is set, at the rate of six per centum per annum for the period of the extension shall be charged and collected on the amount for which any extension of time for payment is granted under this subdivision.

(j) Payment of installments in advance.--A taxpayer may elect to pay any installment of estimated tax or estimated tax surcharge prior to the date prescribed in this section for payment thereof.