Find the amount in a continuously compounded account for the following condition.
Principal, $3000; Annual interest rate, 5.6%; time, 2 years
The balance after 2 years is?
The formula to find the balance in a continuously compounded account is given by the formula:
A = P * e^(rt)
Where:
A = the balance after time t
P = the principal amount
r = the annual interest rate (expressed as a decimal)
t = time in years
e = Euler's number, approximately 2.71828
Given:
P = $3000
r = 5.6% = 0.056
t = 2 years
Plugging in the values into the formula, we get:
A = 3000 * e^(0.056 * 2)
Using a calculator, we find:
A ≈ 3000 * 1.2277103
A ≈ $3,683.13
Therefore, the balance after 2 years in a continuously compounded account is approximately $3,683.13.