Posted by **Bill** on Friday, December 10, 2010 at 12:23am.

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

- Math -
**MathMate**, Friday, December 10, 2010 at 10:24am
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

==============

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 %.

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