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.

Answer 1

To find the amount of money in the account after one year using the formula \( P(t) = 1200 e^{0.16t} \), we substitute \( t = 1 \):

\[ P(1) = 1200 e^{0.16 \times 1} \] \[ P(1) = 1200 e^{0.16} \]

Now, we need to calculate \( e^{0.16} \). The value of \( e^{0.16} \) can be computed using a calculator:

\[ e^{0.16} \approx 1.17351 \]

Now, substitute this value back into the equation:

\[ P(1) = 1200 \times 1.17351 \] \[ P(1) \approx 1408.21 \]

Thus, the amount of money in the account after one year is approximately $1,408.21.