$3000 are deposited in an account with 9% interest rate, compounded continuously. what is the balance after…

Explanation:

Step1: Identify the continuous - compounding formula

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

Step2: Convert the interest rate to decimal

The interest rate $r = 9%=0.09$. The principal amount $P = 3000$ and the time $t = 14$ years.

Step3: Substitute the values into the formula

$A=3000\times e^{0.09\times14}$. First, calculate the exponent: $0.09\times14 = 1.26$. Then, find the value of $e^{1.26}$. Using a calculator, $e^{1.26}\approx3.52437$. Multiply by the principal: $A = 3000\times3.52437=10573.11$.

Answer:

$10573.11$