1. **Problem statement:** An investor contributes 10000 per year, increasing the contribution by 5% each year, for 8 years. The interest rate is 9% per year. We want to find the future value of these contributions. 2. **Formula and explanation:** This is a growing annuity problem. The future value of a growing annuity is given by: $$FV = P \times \frac{(1 + r)^n - (1 + g)^n}{r - g}$$ where: - $P$ is the initial payment (10000), - $r$ is the interest rate (0.09), - $g$ is the growth rate of payments (0.05), - $n$ is the number of periods (8). 3. **Calculate each term:** - Calculate $(1 + r)^n = (1 + 0.09)^8 = 1.09^8$ - Calculate $(1 + g)^n = (1 + 0.05)^8 = 1.05^8$ 4. **Evaluate powers:** - $1.09^8 \approx 1.999004$ - $1.05^8 \approx 1.477455$ 5. **Substitute values into formula:** $$FV = 10000 \times \frac{1.999004 - 1.477455}{0.09 - 0.05} = 10000 \times \frac{0.521549}{0.04}$$ 6. **Calculate fraction:** $$\frac{0.521549}{0.04} = 13.038725$$ 7. **Calculate future value:** $$FV = 10000 \times 13.038725 = 130387.25$$ **Final answer:** The future value of the contributions after 8 years is approximately 130387.25.