The value of the investment at the time \(t + ∆t\) is then given by \[\label{eq:1}S(t+\Delta t)=S(t)+(r\Delta t)S(t)+k\Delta t,\] where at the end of the time interval \(∆t\), \(r\Delta tS(t)\) is the...The value of the investment at the time \(t + ∆t\) is then given by \[\label{eq:1}S(t+\Delta t)=S(t)+(r\Delta t)S(t)+k\Delta t,\] where at the end of the time interval \(∆t\), \(r\Delta tS(t)\) is the amount of interest credited and \(k∆t\) is the amount of money deposited \((k > 0)\) or withdrawn \((k < 0)\).
