Find the amount in a continuously compounded account for the following condition.
Principal, $3000; Annual interest rate, 5.3%; time, 5 years
The balance after 5 years is
The formula for the amount in a continuously compounded account is given by the equation:
A = P * e^(rt)
Where A is the amount, P is the principal, e is Euler's number (approximately 2.71828), r is the annual interest rate as a decimal, and t is the time in years.
Using this formula, we can calculate the amount:
A = 3000 * e^(0.053 * 5)
A ≈ 3000 * e^0.265
A ≈ 3000 * 1.303
A ≈ $3,909.04
Therefore, the balance after 5 years in a continuously compounded account with a principal of $3000 and an annual interest rate of 5.3% is approximately $3,909.04.