$4(20$ points$).\backslash (\backslash$$ $35,000\backslash )$ is deposited in a bank account that pays $\backslash (12\backslash \%\backslash )$ nominal interest per year. $($a$)$ How long does it take for the account to reach $\backslash (\backslash$$ $500,000\backslash ),$ if interest compounds annually?$21\mathrm{.}5$ years $\backslash (21\mathrm{.}5\backslash )$ years $\backslash (22\mathrm{.}5\backslash )$ years $\backslash (23\mathrm{.}5\backslash )$ years $\backslash (24\mathrm{.}5\backslash )$ years Question $9($b$)$ How long does it take for the account to reach $\backslash (\backslash$$ $500,000\backslash ),$ if interest compounds monthly? $19$ years $20$ years $21$ years $22$ years