manuel opened a savings account and deposited $400.00. the account earns 14% interest, compounded…

Explanation:

Step1: Recall continuous - compounding formula

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

Step2: Identify the values of $P$, $r$, and $t$

Given that $P=$400$, $r = 0.14$ (since $14%=0.14$), and $t = 1$ year.

Step3: Substitute the values into the formula

$A=400\times e^{0.14\times1}=400e^{0.14}$.

Step4: Calculate the value of $A$

Using a calculator, $e^{0.14}\approx1.15027$, so $A = 400\times1.15027=$460.108$.

Step5: Round to the nearest cent

Rounding $460.108$ to the nearest cent gives $A\approx$460.11$.

Answer:

$460.11$