jill opened a savings account and deposited $100.00 as principal. the account earns 4% interest, compounded…

Explanation:

Step1: Identify the formula

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

Step2: Convert the interest rate to decimal

The annual interest rate $r = 4%=0.04$, the principal $P = 100$, and the time $t = 5$ years.

Step3: Substitute the values into the formula

$A=100\times e^{0.04\times5}$.

Step4: Calculate the exponent

First, calculate $0.04\times5 = 0.2$. Then, find $e^{0.2}$. Using a calculator, $e^{0.2}\approx1.221403$.

Step5: Calculate the final amount

$A = 100\times1.221403=122.1403$.

Answer:

$122.14$