Initial Value=2.5 Drift rate per annum=0.4 Variance rate per annum=0.5 Standard deviation=(0.5^0.5)= 0.707107 At the end of second year: Mean=2.5+(2*0.4)=3.3 Standard deviation=0.707107*(2^0.5)=1 Double of initial value=2*2.5=5 Z value=(5-mean)/Standard deviation=(5-3.3)/1=1.7 Cumulative area Under the Standard Normal Distribution Table For z value=1.7 Cumulative area=N(d)=0.9554 The probability that cash position will be more than double(greater than 5): (1-0.9554)=0.0446 The probability that cash position will be more than double(greater than 5)=4.46% Cash position negative: Mean=2.5+(2*0.4)=3.3 Standard deviation=0.707107*(2^0.5)=1 Cash position zero=0 Z value=(0-mean)/Standard deviation=(0-3.3)/1=-3.3 Cumulative area Under the Standard Normal Distribution Table For z value=-3.3 Cumulative area=N(d)=0.0013 {Cumulative area N(d) given in table for -3, below -3 is not mentioned in the table. The z value is rounded to -3} The probability that cash position will be negative: =0.0013 The probability that cash position negative=0.13% The probability that cash position will be more than double=4.46% The probability that cash position will be negative=0.13% Solution Initial Value=2.5 Drift rate per annum=0.4 Variance rate per annum=0.5 Standard deviation=(0.5^0.5)= 0.707107 At the end of second year: Mean=2.5+(2*0.4)=3.3 Standard deviation=0.707107*(2^0.5)=1 Double of initial value=2*2.5=5 Z value=(5-mean)/Standard deviation=(5-3.3)/1=1.7 Cumulative area Under the Standard Normal Distribution Table For z value=1.7 Cumulative area=N(d)=0.9554 The probability that cash position will be more than double(greater than 5): (1-0.9554)=0.0446 The probability that cash position will be more than double(greater than 5)=4.46% Cash position negative: Mean=2.5+(2*0.4)=3.3 Standard deviation=0.707107*(2^0.5)=1 Cash position zero=0 Z value=(0-mean)/Standard deviation=(0-3.3)/1=-3.3 Cumulative area Under the Standard Normal Distribution Table For z value=-3.3 Cumulative area=N(d)=0.0013 {Cumulative area N(d) given in table for -3, below -3 is not mentioned in the table. The z value is rounded to -3} The probability that cash position will be negative: =0.0013 The probability that cash position negative=0.13% The probability that cash position will be more than double=4.46% The probability that cash position will be negative=0.13%.