Question

Gabriela invests $1,200 into a continuously compounding account with an annual interest rate of 16 percent. Use the formula P(t)=1,200e0.16t
to determine the amount of money in the account after one year. Include cents, if needed.(1 point)

Answer 1

To determine the amount of money in Gabriela's account after one year using the formula for continuously compounding interest, we can plug in the values into the formula \( P(t) = 1200 e^{0.16t} \).

Here, \( t = 1 \) (one year) and the formula becomes:

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

Calculating \( e^{0.16} \) first:

\[
e^{0.16} \approx 1.17351 \quad (\text{using a calculator})
\]

Now substituting back into the formula:

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

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