Devin deposited $90,000 in an investment fund that was growing at a rate of 6.00% compounded quarterly, for a period of 4 years and 9 months.

**a.** What is the accumulated value of the investment at the end of 4 years and 9 months?

Round to the nearest cent

**b.** What is the amount of interest earned from this investment?

Round to the nearest cent

To solve this problem, we'll use the formula for compound interest, which is given by:

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

where:
- $ A $ is the accumulated value of the investment (the amount after interest),
- $ P $ is the principal amount (initial investment),
- $ r $ is the annual 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 Data:
- $ P = 90,000 $ (initial investment)
- $ r = 6.00\% = 0.06 $
- $ n = 4 $ (since the interest is compounded quarterly)
- $ t = 4 $ years and 9 months

### Step 1: Convert the time to years
Since 9 months is $\frac{9}{12} = 0.75$ years, the total time $ t $ in years is:
\[
t = 4 + 0.75 = 4.75 \text{ years}
\]

### Step 2: Calculate the accumulated value (A)
Substitute the values into the compound interest formula:
\[
A = 90,000 \left(1 + \frac{0.06}{4}\right)^{4 \times 4.75}
\]

### Step 3: Calculate the amount of interest earned
The interest earned is the difference between the accumulated value and the initial principal:
\[
\text{Interest} = A - P
\]

Let's calculate these values.### Results:

**a.** The accumulated value of the investment at the end of 4 years and 9 months is **$119,425.57** (rounded to the nearest cent).

**b.** The amount of interest earned from this investment is **$29,425.57** (rounded to the nearest cent).

Do you want more details or have any questions about the calculations?

Here are 8 related questions to consider:
1. How would the accumulated value change if the interest was compounded monthly instead of quarterly?
2. What if the investment period was extended to 6 years with the same interest rate and compounding frequency?
3. How much would the interest earned change if the initial investment was $100,000 instead of $90,000?
4. What would be the accumulated value if the interest rate was 5% instead of 6%?
5. How does the compounding frequency affect the accumulated value over time?
6. If the investment was compounded annually instead of quarterly, what would the new accumulated value be?
7. How would the results change if Devin withdrew half of the initial investment after 2 years?
8. What would the total value be if Devin made an additional deposit of $10,000 at the beginning of the 3rd year?

**Tip:** The more frequently interest is compounded, the greater the accumulated value will be.

Learn how to calculate compound interest and investment growth for an initial investment of $90,000 at an annual interest rate of 6.00%, compounded quarterly, over 4 years and 9 months. Find out the accumulated value and interest earned with step-by-step calculations.

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