To offer scholarships to children of employees, a company invests $12,000 at the end of every three months in an annuity that pays 1 1 % compounded quarterly.a. How much will the company have in scholarship funds at the end of ten years?b. Find the interest. Determine the $ the company will have in scholarship funds. Round your final answer to the nearest dollar as needed.

This problem involves calculating the future value of an annuity where regular investments are made, and interest is compounded quarterly. Let's break it down:

### Given:
- The company invests $12,000 at the end of every three months (quarterly).
- Interest rate: 11% per year (1 1/11% is interpreted as 11%).
- Compounded quarterly.
- Investment period: 10 years.

### Part a: Calculate the future value of the annuity

The formula for the future value of an ordinary annuity is:

\[
FV = P \times \left(\frac{(1 + r)^n - 1}{r}\right)
\]

Where:
- $ P $ is the regular payment (investment),
- $ r $ is the interest rate per period,
- $ n $ is the total number of periods.

#### Step 1: Identify the variables
- $ P = 12,000 $ (quarterly investment),
- Annual interest rate = 11%, so quarterly interest rate $ r = \frac{11\%}{4} = 0.0275 $,
- Number of periods $ n = 4 \times 10 = 40 $ (since it's compounded quarterly for 10 years).

Now let's compute the future value.

### Part b: Find the total interest earned

The interest earned can be found by subtracting the total amount invested from the future value:

\[
\text{Interest} = FV - (P \times n)
\]

Let me calculate both parts now.### Results:
a. The company will have **$855,218** in scholarship funds at the end of ten years.

b. The total interest earned will be **$375,218**.

Do you have any questions, or would you like further details? 

Here are some related questions to explore further:

1. How would the outcome change if the investment period was 15 years instead of 10?
2. What if the interest was compounded monthly instead of quarterly?
3. How would the total funds change if the interest rate increased to 12%?
4. What if the company contributed $15,000 every three months instead of $12,000?
5. How much would the company need to invest quarterly to reach $1 million in scholarship funds in 10 years?

**Tip**: The frequency of compounding significantly impacts the growth of investments. More frequent compounding results in higher future values.

To offer scholarships to children of employees, a company invests $12,000 at the end of every three months in an annuity that pays 11% compounded quarterly. a. How much will the company have in scholarship funds at the end of ten years? b. Find the interest. Determine the $ the company will have in scholarship funds. Round your final answer to the nearest dollar as needed.

Calculate the future value of an annuity where a company invests $12,000 quarterly at 11% compounded quarterly for 10 years. Find how much the company will have in scholarship funds and the total interest earned. Suitable for advanced financial mathematics students.

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