Find the amount in a continuously compounded account for the following condition, round to the nearest cent as needed.
Principal, $5000; Annual interest rate, 5.5%; time, 4 years.
What is the balance after 4 years?
The formula for continuously compounded interest is given by the equation:
A = P * e^(rt)
where:
A = amount in the account after t years
P = principal amount ($5000 in this case)
e = Euler's number (approximately 2.71828)
r = annual interest rate (5.5% or 0.055 in decimal form)
t = time in years (4 years in this case)
Plugging in the values, we get:
A = $5000 * e^(0.055 * 4)
A = $5000 * e^(0.22)
A ≈ $5000 * 1.246238
A ≈ $6231.19
Therefore, the balance in the continuously compounded account after 4 years would be approximately $6231.19.