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 how much (Round the final answer to the nearest cent as needed. Round all intermediate values to five decimal places as needed.)
To find the amount in a continuously compounded account, we can use the formula:
A = P*e^(rt),
where A is the amount, P is the principal, e is the base of the natural logarithm (approximately 2.71828), r is the annual interest rate, and t is the time in years.
Given:
P = $4000
r = 5.1% = 0.051 (converted to decimal)
t = 3 years
Substituting these values into the formula, we have:
A = 4000 * e^(0.051 * 3)
Calculating e^(0.051 * 3):
e^(0.051 * 3) ≈ 1.16487
Calculating A:
A = 4000 * 1.16487
A ≈ $4659.48
Therefore, the balance after 3 years in the continuously compounded account is approximately $4659.48.