To find the rate of interest, we can use the formula for compound interest:

$A = P \left(1 + \frac{r}{n}\right)^{nt}$

Where:

• $A$ is the amount after interest (final value of the investment),
• $P$ is the principal (initial value of the investment),
• $r$ is the annual interest rate (in decimal form),
• $t$ is the time the money is invested for (in years),
• $n$ is the number of times the interest is compounded per year.

Since the problem does not specify how often the interest is compounded, we will assume it is compounded annually, so $n = 1$.

Given:

• $A = 8046.44$
• $P = 2300$
• $t = 12$
• $n = 1$

We substitute these values into the formula and solve for $r$:

$8046.44 = 2300 \left(1 + \frac{r}{1}\right)^{12}$

First, divide both sides by 2300:

$\frac{8046.44}{2300} = \left(1 + r\right)^{12}$

$3.5 = \left(1 + r\right)^{12}$

Now, take the 12th root of both sides:

$1 + r = \sqrt[12]{3.5}$

$1 + r = 1.1108$

Finally, subtract 1 from both sides:

$r = 0.1108$

Convert this to a percentage:

$r = 11.08\%$

So, the rate of interest is approximately 11.08%.

Would you like more details or have any questions about this solution?

Here are five related questions to further your understanding:

1. What if the interest was compounded quarterly instead of annually?
2. How would the formula change if Elena invested the same amount but for only 8 years?
3. Can you calculate the interest rate if the final value of the investment was $9000 instead of $8046.44?
4. How much would the investment be worth if the rate of interest was 10% instead of 11.08%?
5. How does the interest rate affect the total return over a long-term investment?

Tip: Always clarify the compounding frequency (annually, quarterly, etc.) for a more accurate calculation of compound interest.