tammy opened a savings account and deposited $800.00. the account earns 2% interest, compounded…

Explanation:

Step1: Identify the continuous - compounding formula

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

Step2: Convert the interest rate to decimal form

The interest rate $r = 2%=0.02$, the principal $P = 800$, and the time $t = 1$ year.

Step3: Substitute the values into the formula

Substitute $P = 800$, $r=0.02$, and $t = 1$ into the formula $A = Pe^{rt}$. We get $A=800\times e^{0.02\times1}$.

Step4: Calculate the value of $A$

Using a calculator, $e^{0.02}\approx1.02020134$. Then $A = 800\times1.02020134 = 816.161072$.

Step5: Round to the nearest cent

Rounding $816.161072$ to the nearest cent gives $A\approx816.16$.

Answer:

$816.16$