(2) For taxable years beginning on or after January first, nineteen hundred ninety-nine, every taxpayer subject to tax under paragraph one of subdivision (b) of section fifteen hundred ten of this article shall pay in each such year an amount equal to forty percent of the tax imposed under such article for the second preceding taxable year, if such second preceding year's tax exceeded one thousand dollars. If such second preceding year's tax exceeded one thousand dollars and such taxpayer is subject to the tax surcharge imposed by section fifteen hundred five-a of this article, such taxpayer shall also pay an amount equal to forty percent of the tax surcharge imposed under section fifteen hundred five-a of this article for the second preceding taxable year.

(3) Such amount or amounts described in paragraphs one and two of this subdivision shall be paid with the return required to be filed with respect to such tax or tax surcharge for the preceding taxable year or with an application for extension of the time for filing such return, for taxable years beginning before January first, two thousand sixteen, and shall be paid on or before the fifteenth day of the third month of each taxable year, for taxable years beginning on or after January first, two thousand sixteen.

(b) Other installments. The estimated tax or estimated tax surcharge for each taxable year with respect to which a declaration of estimated tax or a declaration of estimated tax surcharge, respectively, is required to be filed under this article 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 taxable year pursuant to subdivision (a) of this section, 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 taxable year, and is not required to be filed on or before June fifteenth of such year the estimated tax or estimated tax surcharge shown on such declaration, after applying thereto the amounts, if any, paid during the same taxable year pursuant to subdivision (a) of this section, 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 taxable year, and is not required to be filed on or before September fifteenth of such year, the estimated tax or estimated tax surcharge shown on such declaration, after applying thereto the amount, if any, paid in respect of such year pursuant to subdivision (a) of this section 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 two and three 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) Payments after amendment 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 taxable year, any increase in the estimated tax or estimated tax surcharge by reason thereof shall be paid at the time of making such amendment.

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

(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 fifteen hundred thirteen 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 shown 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 section sixteen of the state finance law, if an amount paid pursuant to subdivision (a) of this section exceeds the tax or tax surcharge, respectively, shown on the return required to be filed by the taxpayer for the taxable year during which such amount was paid, interest shall be allowed and paid on the amount by which the amount so paid pursuant to subdivision (a) exceeds such tax or tax surcharge, at the overpayment rate set by the commissioner of taxation and finance pursuant to subdivision (e) of section one thousand ninety-six or, if no rate is set, at the rate of six percent per annum, from the date of payment of the amount so paid pursuant to such subdivision (a) to the fifteenth day of the third 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 loss described in paragraph four of subdivision (b) of section fifteen hundred three.

(f) The second preceding year's tax defined. As used in this section, "the second preceding year's tax" means, for taxpayers subject to tax under subdivision (b) of section fifteen hundred ten of this article, the taxes imposed upon the taxpayer by sections fifteen hundred one and fifteen hundred ten of this article from the second preceding taxable year or as otherwise determined by subdivision (b) of section fifteen hundred five of this article, and for taxpayers subject to tax under section fifteen hundred two-a of this article, the tax imposed upon the taxpayer by such section fifteen hundred two-a of this article from the second preceding year.

(g) Fiscal year. The provisions of this section shall apply to taxable years 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.

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

(i) Extension of time. The commissioner of taxation and finance may grant a reasonable extension of time, not to exceed six months, for the 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 subdivision (e) of section one thousand ninety-six or, if no rate is set, at the rate of six percent 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 the payment thereof.