nicole opened a savings account 4 years ago. the account earns 14% interest, compounded continuously. if the…

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 (initial deposit), $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. We need to solve for $P$. Rearranging the formula gives $P=\frac{A}{e^{rt}}$.

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

We are given that $A = 400$, $r=0.14$ (since $14%=0.14$), and $t = 4$.

Step3: Substitute the values into the formula

$P=\frac{400}{e^{0.14\times4}}=\frac{400}{e^{0.56}}$.

Step4: Calculate the value of $P$

Using a calculator, $e^{0.56}\approx1.75067$. Then $P=\frac{400}{1.75067}\approx228.48$.

Answer:

$228.48$