Doubling and tripling times of a capital

Statement

A capital is invested at a compound interest rate of $3{.}5\%$ per year.

• (a) In how many years does it double?
• (b) In how many years does it triple?

Solution

The amount is $M=C\cdot 1{.}035^{\,n}$.

(a) $1{.}035^{\,n}=2\Rightarrow n=\dfrac{\ln 2}{\ln 1{.}035}=\dfrac{0{.}69315}{0{.}03440}\approx 20{.}15$ years.

(b) $1{.}035^{\,n}=3\Rightarrow n=\dfrac{\ln 3}{\ln 1{.}035}=\dfrac{1{.}09861}{0{.}03440}\approx 31{.}94$ years.

$\boxed{n_2\approx 20{.}15\ \text{years};\qquad n_3\approx 31{.}94\ \text{years}}$