Please help me solve this word problem that involves interest compounded continuously and how long it will take for an investment to double

Question

If an account pays 3.5% interest compounded continuously, how long it will take for an investment to double? (Round your answer to the whole number).

Hint. You can choose the amount of the investment.

Answer 1

Let P = amount of the investment

 

     A(t) = amount after t years

 

Then, A(t) = Pe^0.035t

 

Find t so that A(t) = 2P:   2P = Pe^0.035t

 

                                               2 = e^0.035t

 

                                           ln2 = ln(e^0.035t)

 

                                           ln2 = 0.035t

 

                                            t = ln2/0.035 ≈ 19.8 years