Find the amount in a continuously compounded account for the following condition.
Principal, $4000; Annual interest rate, 5.7%; time, 2 years
The balance after 2 years is $
To find the balance after 2 years in a continuously compounded account, we use the formula:
A = P * e^(rt)
Where:
A is the final balance.
P is the principal amount.
e is Euler's number (approximately 2.71828).
r is the annual interest rate (expressed as a decimal).
t is the time in years.
Using the provided information:
P = $4000
r = 0.057 (5.7% expressed as a decimal)
t = 2
A = 4000 * e^(0.057 * 2)
Using a calculator or math software:
A ≈ $4480.584
Therefore, the balance after 2 years is approximately $4480.584.