To calculate the amount of money accumulated, we will use the compound interest formula:

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

Where:

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

Given:

• $P = 10,000$,
• $r = 0.03$ (3% annual interest),
• $n = 4$ (quarterly compounding),
• $t = 2$ years.

Now, let's calculate $A$.

$A = 10,000 \left(1 + \frac{0.03}{4}\right)^{4 \times 2}$

First, calculate the individual terms:

= 10,000 \left(1 + 0.0075\right)^{8} = 10,000 \left(1.0075\right)^{8}$$ Now, let's compute the value of $$A$$.The accumulated amount of money after 2 years, with an investment of $10,000 at 3% interest compounded quarterly, is approximately **$10,615.99**. Would you like further details or have any questions? Here are 5 related questions you might find useful: 1. How does the frequency of compounding affect the total accumulated amount? 2. What would happen if the interest rate was higher, say 5%? 3. How would the result change if the interest was compounded monthly instead of quarterly? 4. What if the investment duration was 5 years instead of 2? 5. Can the compound interest formula be applied to continuous compounding, and if so, how? **Tip:** The more frequent the compounding, the greater the accumulated amount will be due to interest being applied on interest more often.