1 year ago, noah won some money in the lottery and put it in a bank account that earns 8% interest…

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. Here, $A = 204$, $r=0.08$, and $t = 1$. We need to find $P$.

Step2: Solve for the principal $P$

From $A = Pe^{rt}$, we can rewrite it as $P=\frac{A}{e^{rt}}$. Substituting the values $A = 204$, $r = 0.08$, and $t = 1$ into the formula, we get $P=\frac{204}{e^{0.08\times1}}=\frac{204}{e^{0.08}}$. Since $e^{0.08}\approx1.083287$, then $P=\frac{204}{1.083287}\approx188.31$.

Step3: Calculate the interest earned

The interest earned $I$ is the difference between the final amount $A$ and the principal $P$. So $I=A - P$. Substituting $A = 204$ and $P\approx188.31$ into the formula, we get $I = 204-188.31=15.69$.

Answer:

$15.69$