A sum of money A(t) in a savings scheme earns interest that is compounded continuously at a nominal rate of 5% per annum.
(i) Write the differential equation satisfied by A(t), taking t in years.
(ii) Solve the differential equation to obtain an explicit expression for A(t) in terms of the initial amount A0.
(iii) Calculate the time, to two decimal places, for the amount to reach 1.5A0.