[tex]ans \to= 282.5[/tex]
[tex]let \: his \:current \: balance \: be : b = 305\to \\ let \: the \: banks \: charge \: fee \: be: f = 7.5 \to\\ let \: his \: balance \: at \: the \: first \: month \: be : b_{1}\to\\ let \: his \: balance \: at \: the \: second \: month \: be : b_{2}\to \\ let \: his \: balance \: at \: the \: fanal \: month \: be : b_{3}\to \\ \\ then \: his \: balance \: in \: 1 {}^{th} \: month \: is \: : \\ b_{1} = b - f \: (this \: due \: to \: his \: current \: balance \: is \: less \: than \: 500) \to \\ b_{1} = 305 - 7.5 = 297.5 \\ \\ his \: balance \: in \: the \: 2 {}^{nd} \: month \: is : \\ b_{2} = b_{1} - f \: (this \: due \: to \: his \: current \: balance \: is \: also \: less \: than \: 500) \to \\ b_{2} = 297.5 - 7.5 = 290 \\ \\ his \: final \: balance \: in \: the \: 3{}^{rd} \: month \: is : \\ b_{3} = b_{2} - f \: (this \: due \: to \: his \: current \: balance \: is \: also \: less \: than \: 500) \to \\ b_{3} = 290 - 7.5 = 282.5 \\ \\ therefore \: his \: final \: balance \: at \: the \: third \: month \: is : \to \: 282.5[/tex]
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