I would like my investment to double in value every 3 years. At what rate of interest would I need to invest it, assuming the interest is compounded continuously?

Answer 1

google "rule of 72"

Answer 2

or, use the compound interest formula
A(t) = Pe^rt
we want the amount to double in three years.

2P = Pe^3r
2 = e^3r
ln 2 = 3r
r = ln2/3 = 0.231

so, the rate is 23.1%

The rule of 72 would give 24%, which is pretty close.