Linear Simultaneous Equation For Stock Trading

Problem An investor bought Company A share (Stock) at securities company 5000 Shares at price $ 1.0/share. When the price went up to $ 1.1/share , all shares were sold. The investor got profit $463. At the same securities company the investor also bought Company B 10000 shares at price $1.5/share . When the price went up to $1.6/share , all shares were sold. The investor got profit $891. Find purchasing fee and selling fee respectively charged by the securities company? Answer. Formula for Profit of stock trading is : U = (1-%Fj) x Nx Hjl - (1+%Fb) x N x Hbl where U=Profit or Loss HJ (Selling Price/Harga Jual)= N x Hjl where N=Number of shares and Hjl=Selling price per share (harga jual perlembar) Hb (Purchasing Price/Harga beli)= N x Hbl where Hbl=(Purchasing Price/ per share (harga beli perlembar) Fj (Selling Fee ) = %Fj x HJ Fb (Purchasing Fee) = %Fb x Hb First Step (Establish Linear Simultaneous Equations) (1) 463 = (1-%Fj) x 5000 x 1.1 - (1+%Fb) x 5000 x 1.0 ⇔ 463=5500 - 5500 %Fj -5000 -5000%Fb ⇔ 5500 %Fj +5000%Fb = 37 (2) 891 = (1-%Fj) x 10000 x 1.6 - (1+%Fb) x 10000 x 1.5 ⇔ 891=16000 - 16000 %Fj -15000 -15000%Fb ⇔ 16000 %Fj +15000%Fb = 109 Second Step (Find Solution of Linear Simultaneous Equations) (1) … 5500 %Fj + 5000%Fb = 37 x 3 (2) ….16000 %Fj +15000%Fb = 109 x 1 ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ 500 %Fj =2 %Fj = 0.004 =0.4%

(1) … 5500 x 0.4% + 5000%Fb = 37 22 +5000%Fb = 37 5000%Fb = 15 %Fb = 0.003=0.3% So, the purchasing fee is 0.03% and the selling fee is 0.04%