Question

how long will it take $5000 to double if it is invested at 6% interest compounded continually? (A=Pe^rt)

Answer 1

The formula is
years = log (total) - log(principal) / log(1+rate)

First, let's figure out 6% compounded continuously
Annual Rate = e^r -1
Annual Rate = (2.718281828^.06)-1
Annual Rate = 0.0618365465

years = [log (10,000) - log (5,000)] / log(1.0618365465)
years = (4 - 3.6989700043) / 0.0260576689
years = 0.3010299957 / 0.0260576689
years = 11.5525