clarence opened a savings account and deposited $10,000.00 as principal. the account earns 14% 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 $r = 14%=0.14$, the principal $P = 10000$, and the time $t = 1$ year.

Step3: Substitute values into the formula

Substitute $P = 10000$, $r = 0.14$, and $t = 1$ into the formula $A = Pe^{rt}$. We get $A=10000\times e^{0.14\times1}$.

Step4: Calculate the value

Using a calculator, $e^{0.14}\approx1.15027$. Then $A = 10000\times1.15027 = 11502.71$.

Answer:

$11502.71$