If $8,500 is invested at 6% compounded continuously, how long will it take to double the investment?

Answer 1

Continuous compounding:
future value = present value * e^rt
where t=number of periods, and r=rate

future value/present value = 2
or
e^rt=2
e^0.06t=2
take natural log on both sides,
0.06t = ln(2)
t=11.55 years.

The rule of 69
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In fact, you can apply the rule of 69 for continuous compounding:
the time (in years) to double is 69.31 divided by the annual rate in %.