brad opened a savings account 1 year ago. the account earns 12% 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 are given that $A=$100$, $r = 0.12$ (since $12%=0.12$), and $t = 1$. We need to solve for $P$.

Step2: Rearrange the formula for $P$

From $A = Pe^{rt}$, we can solve for $P$ by dividing both sides of the equation by $e^{rt}$. So, $P=\frac{A}{e^{rt}}$.

Step3: Substitute the given values

Substitute $A = 100$, $r=0.12$, and $t = 1$ into the formula for $P$. We get $P=\frac{100}{e^{0.12\times1}}=\frac{100}{e^{0.12}}$.

Step4: Calculate the value of $P$

Using a calculator, $e^{0.12}\approx1.127497$. Then $P=\frac{100}{1.127497}\approx88.78$.

Answer:

$88.78$