Question

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

Answer 1

At `8.66%`

Explanation:

An investment of `x` with continuously compounded interest at `r` (`r` expressed as fraction not in percentage term) is `xe^(rt)` in `t` years.

As it doubles in `8` years, we have `xe^(8r)=2x`

or `e^(8r)=2`

or `8r=ln2=0.69315`

or `r=0.69315/8=0.0866=8.66%`