$1100 are deposited in an account with 5.8% interest rate, compounded continuously. what is the balance…

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 form

Given $r = 5.8%=0.058$, $P=$1100$, and $t = 22$ years.

Step3: Substitute the values into the formula

$A=1100\times e^{0.058\times22}$. First, calculate the exponent: $0.058\times22 = 1.276$. Then, find $e^{1.276}$. Using a calculator, $e^{1.276}\approx3.5737$. Now, $A = 1100\times3.5737$. $A=1100\times3.5737 = 3931.07$.

Answer:

$3931.07$