Border Security Investment Act This bill imposes a fee on remittances sent to certain countries and provides funding for border security activities from the collected amounts. Specifically, the fee shall apply to remittances sent to one of the five countries that had the most citizens or nationals unlawfully enter the United States in the previous fiscal year, as determined by U.S. Customs and Border Protection. The fee must be 37% of the amount sent. Half of the money collected by the fee must be placed in a trust fund for reimbursing border states for expenses incurred for border security enforcement measures. The other half must be placed in another trust fund for (1) deploying technology and installing physical barriers along the U.S.-Mexico border, and (2) paying the wages and salaries of U.S. Border Patrol agents. If the amount in the trust funds exceeds a certain threshold, the excess money must be used only for deficit reduction.