\( \$ 900 \) are deposited in an account with 70, interest rate, compounded continuously. What is the balance after 6 years? \[ F=\$[?] \]

To find the balance after 6 years with continuous compounding, you can use the formula \( F = Pe^{rt} \), where \( P \) is the principal amount (\$900), \( r \) is the interest rate (0.70), and \( t \) is the time in years (6). Plugging in the numbers, we calculate: \[ F = 900e^{(0.70)(6)} \approx 900 \times e^{4.2} \approx 900 \times 66.6863 \approx 60,018.76 \] So the balance after 6 years is approximately \( F = \$60,018.76 \). Isn't it fascinating how money can grow exponentially with continuous compounding? Just think about it; spending years parked in a bank can turn into a mini fortune if nurtured with high interest rates! For a real-world twist, this principle applies to investments as varied as retirement accounts or savings plans. Imagine putting away some cash into a fund that compounds continuously; it’s like planting a money tree that keeps growing! Now, wouldn't you want to be a savvy investor like that?