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Emmett deposited $90$ $\$$ in an account earning $5\%$ interest compounded annually. To the nearest cent, how much will he have in $2$ years? Use the formula $B = p(1 + r)^t$, where $B$ is the balance (final amount), $p$ is the principal (starting amount), $r$ is the interest rate expressed as a decimal, and $t$ is the time in years. $\$$____