Find the amount in a continuously compounded account for the following condition.
Principal, $2000; Annual interest rate, 5.2%; time, 5 years
the balance after 5 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 calculating the balance in a continuously compounded account is given by the formula:
A = P * e^(rt)
Where:
A = balance after time t
P = principal amount
r = annual interest rate (as a decimal)
t = time in years
e = Euler's number (approximately 2.71828)
Using the given values:
P = $2000
r = 5.2% = 0.052 (as a decimal)
t = 5 years
A = 2000 * e^(0.052 * 5)
Calculating this value using a calculator, we find that the balance after 5 years is approximately $2673.15.