jill is saving up money to buy a car. jill puts $10,000.00 into an account which earns 4% interest…

Explanation:

Step1: Identify the 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

Given $r = 4%=0.04$, $P=$10000$, and $t = 1$ year.

Step3: Substitute values into the formula

$A=10000\times e^{0.04\times1}=10000e^{0.04}$.

Step4: Calculate the value

Using a calculator, $e^{0.04}\approx1.04081077$, so $A = 10000\times1.04081077=$10408.11$.

Answer:

$10408.11$