Time to double at six percent

Statement

In how many years does a capital double at $6\%$ per year with compound interest?

Solution

From $(1{.}06)^{t}=2$ we get $t\ln 1{.}06=\ln 2$. $t=\frac{\ln 2}{\ln 1{.}06}=\frac{0{.}693147}{0{.}058269}\approx\boxed{11{.}90\ \text{years}}.$