manuel opened a savings account and deposited $600.00. the account earns 5% 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=$600$, $r = 0.05$ (since $5%=0.05$), and $t = 1$ year.

Step3: Substitute the values into the formula

$A=600\times e^{0.05\times1}=600\times e^{0.05}$.

Step4: Calculate the value of $A$

Using a calculator, $e^{0.05}\approx1.051271$. Then $A = 600\times1.051271=$630.7626$.

Step5: Round to the nearest cent

Rounding $630.7626$ to the nearest cent gives $A\approx$630.76$.

Answer:

$630.76$