What interest rate is required for an investment with continuously compounded interest to double in 8 years?

Oct 31, 2016

At 8.66%

Explanation:

An investment of $x$ with continuously compounded interest at $r$ ($r$ expressed as fraction not in percentage term) is $x {e}^{r t}$ in $t$ years.

As it doubles in $8$ years, we have $x {e}^{8 r} = 2 x$

or ${e}^{8 r} = 2$

or $8 r = \ln 2 = 0.69315$

or r=0.69315/8=0.0866=8.66%