jessica opened a savings account and deposited $100.00 as principal. the account earns 10% interest…

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 $r = 10%=0.1$. The principal $P = 100$, and the time $t = 5$ years.

Step3: Substitute the values into the formula

Substitute $P = 100$, $r=0.1$, and $t = 5$ into the formula $A = Pe^{rt}$. We get $A=100\times e^{0.1\times5}$.

Step4: Calculate the value of $A$

First, calculate the exponent: $0.1\times5 = 0.5$. Then, find the value of $e^{0.5}$. Using a calculator, $e^{0.5}\approx1.648721$. Multiply by the principal: $A = 100\times1.648721=164.8721$.

Step5: Round the answer

Rounding $164.8721$ to the nearest cent, we get $A\approx164.87$.

Answer:

$164.87$