Find to the nearest tenth of a year how long it will take to DOUBLE an investment when it is invested at 5.5% compounded continuously.

Question

P=Ae^rt

 

For interest compounded continuously, the total amount P is given by P=Ae^rt where A is the initial amount invested, r is the yearly rate and t is the time in years.Find to the nearest tenth of a year how long it will take to DOUBLE an investment when it is invested at 5.5% compounded continuously.

Answer 1

P = Ae^0.055t

 

The investment doubles when P = 2A

 

So, we must find t so that 2A = Ae^0.055t

 

                                       2 = e^0.055t

 

                                   ln2 = ln(e^0.055t)

 

                                   ln2 = 0.055t

 

                                      t = ln2/0.055 ≈ 12.6 years