find the amount in a continuously compounded account for the following condition. principal, $2000; annual…

find the amount in a continuously compounded account for the following condition. principal, $2000; annual interest rate, 5.7%; time, 2 years the balance after 2 years is $ (round the final answer to the nearest cent as needed. round all intermediate values to five decimal places as needed.)

find the amount in a continuously compounded account for the following condition. principal, $2000; annual interest rate, 5.7%; time, 2 years the balance after 2 years is $ (round the final answer to the nearest cent as needed. round all intermediate values to five decimal places as needed.)

Answer

Explanation:

Step1: Identify the formula

The formula for continuous - compounding is $A = Pe^{rt}$, where $A$ is the amount of money in the account after $t$ years, $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the number of years.

Step2: Convert the interest rate to decimal

Given $r = 5.7%=0.057$, $P = 2000$, and $t = 2$.

Step3: Substitute values into the formula

$A=2000\times e^{0.057\times2}$. First, calculate the exponent: $0.057\times2 = 0.114$. Then, find the value of $e^{0.114}$. Using a calculator, $e^{0.114}\approx1.12086$. Now, $A = 2000\times1.12086=2241.72$.

Answer:

$2241.72$