The county treasurer shall use the proceeds of the supplemental assessment or of the warrant delivered to him pursuant to Section 52559, as the case may be, for the following purposes:
(a)
The payment of any amount by which the total amount necessary to pay the principal and accrued interest on the bonds next maturing exceeds the proceeds from the sale of the refunding bonds, exclusive of accrued interest.
(b)
The payment to the purchaser of the refunding bonds at the time he takes delivery thereof, of interest at the rate provided in the
refunding bonds from the date the sale is completed by the payment of the purchase price until the date when, pursuant to the terms of the refunding bonds and the coupons thereto attached, interest thereon shall begin to accrue.