Max invest $\$P$ in a bank where amount compounds annually at the rate of $r\%$. If he plans to invest for $t$ years, the amount he will get after $t$ years is $\begin{align*} A = P \begin{pmatrix}1+\frac{r}{100}\end{pmatrix}^t \end{align*}$. In how many years will his amount double ?

Question

$\begin{array}{1 1} (a)\; 10\; years \\ (b)\; 10.5 \;years \\ (c)\; 12\;years \\ (d)\; 12.5 years \end{array}$