If property other than money is delivered to the administrator under this part, the owner shall be entitled to receive from the administrator any income or gain realized or accruing on the property at or before liquidation or conversion of the property into money. If the property was an interest-bearing demand, savings, or time deposit, including a deposit that is automatically renewable, the administrator shall pay simple interest at the legal rate of interest established in section 478-2, or any lesser rate the property earned while in the possession of the administrator. Interest shall begin to accrue when the property is delivered to the administrator and ceases on the earlier of the expiration of ten years after delivery or the date on which payment is made to the owner. Interest on interest-bearing property shall not be payable for any property delivered to the administrator before July 1, 2009.