Let's break this down and calculate the interest for both Joanna and Trea based on the information provided:

Joanna's Interest (Compounded Yearly)

Joanna's account earns 2% interest compounded yearly. The formula for compound interest is:

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

Where:

• $A$ is the amount of money accumulated after $t$ years, including interest.
• $P$ is the principal amount (initial deposit), which is $3,000.
• $r$ is the annual interest rate (decimal form), so $2\% = 0.02$.
• $n$ is the number of times the interest is compounded per year (in this case, yearly, so $n = 1$).
• $t$ is the time the money is invested, which is 2 years.

Plugging the values into the formula:

$A = 3000 \left(1 + \frac{0.02}{1}\right)^{1 \times 2}$

$A = 3000 \times (1.02)^2$

$A = 3000 \times 1.0404$

$A = 3121.20$

So, Joanna's total amount after 2 years is $3,121.20. The interest earned is:

$\text{Interest} = A - P = 3121.20 - 3000 = 121.20$

Trea's Interest (Simple Interest)

Trea's account earns 2.5% simple interest. The formula for simple interest is:

$I = P \times r \times t$

Where:

• $I$ is the interest earned.
• $P$ is the principal amount (initial deposit), which is $3,000.
• $r$ is the annual interest rate (decimal form), so $2.5\% = 0.025$.
• $t$ is the time the money is invested, which is 2 years.

Plugging the values into the formula:

$I = 3000 \times 0.025 \times 2$

$I = 3000 \times 0.05$

$I = 150$

So, Trea earns $150 in interest after 2 years.

Final Results

• Joanna's interest: $121.20 (compounded yearly).
• Trea's interest: $150 (simple interest).

If you're selecting from drop-down menus, based on this information, the answers will likely be:

1. Joanna will have earned $121.20 in interest.
2. Trea will have earned $150 in interest.

Would you like more details on this or help with any other part of the problem?

Here are 5 related questions to expand on:

1. What happens to the interest if Joanna's account compounds quarterly instead of yearly?
2. How would Trea’s interest change if her account used compound interest instead of simple interest?
3. What would the final amount be in Joanna's account after 5 years?
4. How does the frequency of compounding affect the total interest earned?
5. What is the difference between simple interest and compound interest in the long run?

Tip: Compound interest grows your money faster than simple interest because it earns interest on both the initial principal and the interest already earned.