The tax imposed by this chapter is due and payable 15 months after the decedent's death and shall be paid by the executor to the department. If the department finds that the payment on the due date of tax or any part of the tax would impose undue hardship upon the estate, the department may extend the time for payment of any part, but no extension may be for more than one year and the aggregate of extensions with respect to an estate may not exceed five years from the due date. In that case, the amount in respect of which the extension is granted shall be paid on or before the date of the expiration of the period of the extension unless a further extension is granted. If the time for the payment is extended, there shall be collected, as part of this amount, interest on the tax as provided in AS 43.05.225(1) from the due date of the tax to the date the tax is paid.