بسم الله الرحمن الرحيم
The interest money which one receives from any government bank account may be paid in income tax (taxes which are forcefully imposed on people). Similarly, it could also be given to any poor without the intention of reward. The poor may use the money in whatsoever need he wishes. Interest money cannot be used in any other place. The stand of your friend that interest money cannot be used in any other place except paying interest is not completely right as interest received from government bank cannot be used in paying the interest of private bank and vice versa. Yes, you may pay interest received from government bank in the interest of government bank. Similarly, interest received from private bank may be used in paying the interest of private bank provided both private banks belong to the same company.
ويردونها على أربابها إن عرفوهم وإلا تصدقوا بها : لأن سبيل الكسب الخبيث التصدق إذا تعذر الرد على صاحبه . (شامى 9/553، زكريا)
Allah knows Best!
Darul Uloom Deoband