Step 1 :Given the formula: \(V = P e^{rt}\), where \(V\) is the value of the account, \(P\) is the principal, \(r\) is the interest rate, and \(t\) is the time in years.
Step 2 :Plug in the values: \(P = 38100\), \(r = 0.04\), and \(t = 9\) into the formula.
Step 3 :Calculate the value of the account: \(V = 38100 e^{(0.04)(9)}\)
Step 4 :Evaluate the expression: \(V \approx 54609.85\)
Step 5 :\(\boxed{54,609.85}\) is the amount of money in the account after 9 years, to the nearest cent.