How long, to the nearest year, will it take an investment to triple if it is continuously compounded at 6% per year?

Nov 18, 2017

To the nearest year, it will it take $18$ years for an investment to triple, if it is continuously compounded at 6% per year.

Explanation:

An investment $P$ compounded continuously at a rate of interest of r% per year for $t$ years becomes

$P {e}^{r t}$, where $e$ is the Euler's number, an irrational number, after Leonhard Euler whose value is $2.71828182845904523536 \ldots .$ and logarithm to base $e$ is mentioned as $\ln$, known as natural log.

As in $t$ years, investment triples, it becomes $3 P$

Hence $P {e}^{0.06 t} = 3 P$

or ${e}^{0.06 t} = 3$

i.e. $0.06 t = \ln 3 = 1.0986122887$

therefore $t = \frac{1.0986122887}{0.06} = 18.31$

hence to the nearest year, it will it take $18$ years for an investment to triple, if it is continuously compounded at 6% per year.