https://file.aiquickdraw.com/mathbot/file/1730178424092ev3vifzh.jpg

To solve this problem, we can use the **Future Value of an Annuity formula** since the company deposits a fixed amount annually:

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

where:
- $ P = 6000 $ (the annual deposit),
- $ r = 0.08 $ (the interest rate per year),
- $ n = 10 $ (the number of years).

### Calculation

Substitute the values into the formula:

\[
FV = 6000 \times \frac{(1 + 0.08)^{10} - 1}{0.08}
\]

Calculating step-by-step:

1. $ 1 + 0.08 = 1.08 $,
2. $ (1.08)^{10} \approx 2.1589 $,
3. $ 2.1589 - 1 = 1.1589 $,
4. $ \frac{1.1589}{0.08} \approx 14.486 $,
5. $ FV = 6000 \times 14.486 \approx 86919.12 $.

### Conclusion

The total amount in the fund after 10 years will be approximately **$86,919**, so the correct answer is:

- **c. $86,919**

Would you like further details, or do you have any questions?

---

Here are five related questions to expand your understanding:

1. How would the answer change if the interest rate was 10% instead of 8%?
2. What if the deposits were made at the beginning of each year instead of the end?
3. How does the Future Value of an Annuity formula differ from the Present Value formula?
4. What is the impact of doubling the deposit amount to $12,000 annually?
5. How would we calculate the total interest earned over the 10 years?

**Tip:** Remember that the Future Value of an Annuity formula applies when periodic deposits are made with a consistent interest rate.

A company deposits $6000 into a fund at the end of each year for 10 years. If the interest rate is 8% per annum, how much will be in the fund after 10 years?

Learn how to calculate the future value of an annuity with $6000 annual deposits over 10 years at an 8% interest rate. This problem covers key finance and compound interest concepts. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation