8.4  Compound Interest

How to determine the value of time(t) when unknown

Example - Compounded continuously

    How long will it take for an investment to double in value if it earns 5% compounded continuously? 

  Given:    r = 0.05

   Find:      t (time)

Work

    A = Pert

   2P = Pe(0.05t)         2P -> the principle is doubled, so we multiply the principal by 2.

   2 = e(0.05t)             Divide both sides by P

  ln 2 = ln e(0.05t)       Because we have e, we need to take the ln of both sides.

 ln 2 = 0.05t  

 ln 2/(0.05) = t        Solve for t (keep your answer in exact form)