# Math

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

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1. Continuous compounding:
future value = present value * ert
where t=number of periods, and r=rate

future value/present value = 2
or
ert=2
e0.06t=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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