To determine the amount of money in the account after one year using the formula for continuous compounding, we use the given formula:
\[ P(t) = 1200e^{0.16t} \]
where \( P(t) \) is the amount of money in the account after \( t \) years, \( e \) is the base of the natural logarithm (approximately 2.71828), and \( t \) is the time in years.
For \( t = 1 \):
\[ P(1) = 1200e^{0.16 \cdot 1} = 1200e^{0.16} \]
Now, we need to calculate \( e^{0.16} \):
\[ e^{0.16} \approx 1.17351 \]
Now, substitute this value back into the equation:
\[ P(1) = 1200 \times 1.17351 \approx 1408.21 \]
Thus, the amount of money in the account after one year is approximately:
\[ \boxed{1408.21} \]