Find the amount in a continuously compounded account for the following conditions
Principal, $4000; Annual interest rate, 5.1%; time, 3 years.
The balance after 3 years is $
. (Round the final answer to the nearest cent as needed. Round all intermediate values to five decimal places as needed.)
The formula for the amount in a continuously compounded account is given by the formula:
A = P * e^(rt)
Where:
A = final amount
P = principal (initial amount)
e = Euler's number (approximately 2.71828)
r = annual interest rate (as a decimal)
t = time (in years)
Plugging in the given values, we have:
A = 4000 * e^(0.051 * 3)
Using a calculator, we can evaluate e^(0.051 * 3) ≈ 1.16487.
A = 4000 * 1.16487
A ≈ 4659.48
Therefore, the balance after 3 years is approximately $4659.48