A $$2$ million deposit earns $7$ percent for $13$ years. If the account earns $9$ percent per year forever after that, how long will it take to grow to $$5$ million?

zero; the account exceeds $$5$ million after $13$ years

$0\mathrm{.}26$ year

$0\mathrm{.}43$ year

$1\mathrm{.}18$ years