(* the data *)
bankdataannual  :=  
        List[{0,  100},  {1,  105.4},  {2,  111.09},  {3,  
            117.09},  {4,  123.41}, {5, 
            130.08}]
bankdatacontin  :=  
      List[{0,  100},  {1,  105.55},  {2,  111.4},  {3,  
          117.59},  {4,  124.11}, {5, 131}]

(* the plot of the annually compounded data *)
p1  =  
        ListPlot[bankdataannual,  
          PlotStyle -> {PointSize[0.02],  RGBColor[1, 0, 0]},  
          PlotRange -> {{0,  6},  {99,  132}},  
          PlotLabel ->  "Balance vs. Time",  
          AxesLabel -> {"Time (y)", "Balance ($)"},  
          TextStyle -> {FontSize -> 18}]

(* You may want to attempt to model this data with a linear equation .   The result is below,  
        taking the slope from the first two data points *)

Show[p1,  Plot[5.4  t  +  100,  {t,  0,  6}]]

(* the continuously compounded data *)

p2  =  
      ListPlot[bankdatacontin,  
        PlotStyle -> {PointSize[0.02],  RGBColor[1, 0, 0]},  
        PlotRange -> {{0,  6},  {99,  132}},  
        PlotLabel ->  "Balance vs. Time",  
        AxesLabel -> {"Time (y)", "Balance ($)"},  
        TextStyle -> {FontSize -> 18}]

(* the annual model *)

Va[t_] :=  100*1.054^t
p3 = 
      Plot[Va[t],  {t,  0,  
          6},   PlotRange -> {{0,  6},  {99,  132}}]

(* the annual model plotted with the data *)

Show[p1,  p3]

(* the continuously compounded data *)

Vc[t_] :=  100*E^(0.054  t)
p4 = 
      Plot[Vc[t],  {t,  0,  
          6},   PlotRange -> {{0,  6},  {99,  132}}]

(* the continuously compounded model with the data *)

Show[p2,  p4]

(* the annual model plotted over 30 years *)

p5 = 
      Plot[Va[t],  {t,  0,  
          30},   PlotRange -> {{0,  30},  {99,  500}},  
        PlotStyle -> {RGBColor[0, 1, 0]}]

(* the continuous model plotted for 30 years *)

p6 = 
      Plot[Vc[t],  {t,  0,  
          30},   PlotRange -> {{0,  30},  {99,  500}},  
        PlotStyle -> {RGBColor[1, 0, 0]}]

(* Both the annually compounded (green) and continuously compounded (red) for 30 years *)

Show[p5,  p6]

Va[30]
Vc[30]

(* the data for the precise rates of change,  
          each to two decimal places *)
bankratedataannual  :=  
        List[{0,  5.26},  {1,  5.54},  {2,  5.84},  {3,  
            6.16},  {4,  6.49}, {5, 
            6.84}]
bankratedatacontin  :=  
      List[{0,  5.4},  {1, 5.70},  {2,  6.02},  {3,  6.35},  {4,  
          6.70}, {5, 7.07}]

(* a plot of the annually compounded rates *)

p7  =  
      ListPlot[bankratedataannual,  
        PlotStyle -> {PointSize[0.02],  RGBColor[1, 0, 0]},  
        PlotRange -> {{0,  6},  {5.2,  6.9}},  
        PlotLabel ->  "Rate of Change of Balance",  
        AxesLabel -> {"Time (y)", "Change in Balance ($/y)"},  
        TextStyle -> {FontSize -> 18}]

(* another attempt at a linear fit *)

Show[p7,  Plot[5.26  +  0.28  t,  {t,  0,  6}]]

(* The actual exponential fit of the annually compounded rate data *)

Show[p7,  Plot[100*Log[1.054]*1.054^t,  {t,  0,  6}]]

(* a plot of the continuously compounded rates *)

p8  =  
      ListPlot[bankratedatacontin,  
        PlotStyle -> {PointSize[0.02],  RGBColor[1, 0, 0]},  
        PlotRange -> {{0,  6},  {5.2,  6.9}},  
        PlotLabel ->  "Rate of Change of Balance",  
        AxesLabel -> {"Time (y)", "Change in Balance ($/y)"},  
        TextStyle -> {FontSize -> 18}]

(* another attempt at a linear fit *)

Show[p8,  Plot[5.4  +  0.3  t,  {t,  0,  6}]]

(* The actual exponential fit of the continuously compounded rates *)

Show[p8,  
      Plot[0.054*100*E^(0.054  t),  {t,  0,  6}]]