Manny invests $\backslash (\backslash$$ $100\backslash )$ in an account that is compounded continuously at an annual interest rate of $\backslash (2\backslash \%\backslash ),$ according to the formula $\backslash ($ A$=$P e$^\{$r t$\}\backslash ),$ where $\backslash ($ A $\backslash )$ is the amount accrued, $\backslash ($ P $\backslash )$ is the principal, $\backslash ($ r $\backslash )$ is the rate of interest, and $\backslash ($ t $\backslash )$ is the time, in years. In $20$ years, how much will Manny's investment be worth to the nearest dollar?

$(1$ point$)$

$\backslash$$$122$

$\backslash$$$149$

$\backslash$$$5,460$

$\backslash$$$102$