Erin deposited $10,000 in an investment fund that was growing at a rate of 2.50% compounded quarterly, for a period of 3 years and 6 months.
a. What is the accumulated value of the investment at the end of 3 years and 6 months?
Round to the nearest cent

To calculate the accumulated value of Erin's investment, we can use the formula for compound interest:

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

Where:
- $ A $ is the accumulated value of the investment.
- $ P $ is the principal amount (initial investment).
- $ r $ is the annual nominal interest rate (as a decimal).
- $ n $ is the number of times the interest is compounded per year.
- $ t $ is the time the money is invested for, in years.

Given:
- $ P = 10,000 $
- $ r = 2.50\% = 0.025 $
- $ n = 4 $ (since the interest is compounded quarterly)
- $ t = 3.5 $ years (which is 3 years and 6 months)

Now, we can substitute these values into the formula:

\[
A = 10,000 \left(1 + \frac{0.025}{4}\right)^{4 \times 3.5}
\]

Let's calculate this step by step.The accumulated value of Erin's investment at the end of 3 years and 6 months is approximately **$10,911.45**.

Would you like further details on this calculation or have any other questions?

Here are some related questions:
1. How does the compound interest formula differ from simple interest?
2. What would the accumulated value be if the interest were compounded monthly instead of quarterly?
3. How does increasing the investment period affect the accumulated value?
4. What would the accumulated value be after 5 years instead of 3.5 years?
5. How does the interest rate affect the accumulated value?
6. What if Erin invested in a fund with a 3% interest rate instead?
7. How does compound interest differ when compounded annually versus quarterly?
8. How much interest is earned over the 3.5 years?

**Tip:** When dealing with compound interest, the frequency of compounding can significantly impact the final amount, especially over long periods.

Learn how to calculate compound interest with quarterly compounding using a real investment example. Erin deposited $10,000 in an investment fund growing at 2.50% annually, compounded quarterly for 3.5 years. Discover the accumulated value at the end of the investment period. Explore the impact of compound interest frequency and time on investment returns.

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