Gabriela invests $1,200 into a continuously compounding account with an annual interest rate of 16 percent. Use the formula P(t)=1,200e^0.16t to determine the amount of money in the account after one year. Include cents, if needed. (1 point) $

1 answer

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:

\[ \boxed{1408.21} \]