Question

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

Answer 1

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

`Pe^(rt)`, where `e` is the Euler's number, an irrational number, after Leonhard Euler whose value is `2.71828182845904523536....` and logarithm to base `e` is mentioned as `ln`, known as natural log.

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

Hence `Pe^(0.06t)=3P`

or `e^(0.06t)=3`

i.e. `0.06t=ln3=1.0986122887`

therefore `t=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.