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

Question

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 the account after one year using the formula for continuous compounding, we can substitute \( t = 1 \) into the formula \( P(t) = 1200 e^{0.16t} \).

First, we need to calculate \( 0.16 \cdot 1 \): \[ 0.16 \cdot 1 = 0.16 \]

Now, we calculate \( e^{0.16} \). The mathematical constant \( e \) is approximately equal to 2.71828. Let's calculate \( e^{0.16} \): \[ e^{0.16} \approx 1.17351 \]

Now, we can substitute this value back into the formula: \[ P(1) = 1200 \cdot e^{0.16} \approx 1200 \cdot 1.17351 \]

Calculating that gives: \[ P(1) \approx 1200 \cdot 1.17351 \approx 1408.21 \]

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