9 years ago, charlie won some money in the lottery and put it in a bank account that earns 12% interest…

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $A$ is the final amount, $P$ is the principal amount, $r$ is the annual interest rate (in decimal), $n$ is the number of times interest is compounded per year, and $t$ is the number of years. Here, $A = 300$, $r=0.12$, $n = 4$ (compounded quarterly), and $t = 9$.

Step2: Solve for the principal $P$

We can rewrite the formula as $P=\frac{A}{(1 +\frac{r}{n})^{nt}}$. Substitute the values: $(1+\frac{0.12}{4})^{4\times9}=(1 + 0.03)^{36}$. Calculate $(1 + 0.03)^{36}\approx2.93172$. Then $P=\frac{300}{2.93172}\approx102.329$.

Step3: Calculate the interest earned

The interest earned $I=A - P$. Substitute $A = 300$ and $P\approx102.329$. So $I=300 - 102.329 = 197.671\approx197.67$.

Answer:

$197.67$