1. **Stating the problem:** We want to evaluate the expression $$P = (1 - 0.25) \times 800 \times a_5^{\left(\frac{2}{5}\right)} + 10,000 \times v^5$$ at an interest rate of 10%, where $$a_5^{\left(\frac{2}{5}\right)}$$ is the present value of an annuity factor and $$v = (1 + i)^{-1}$$ is the discount factor. 2. **Formula and explanation:** - The term $a_5^{\left(\frac{2}{5}\right)}$ represents the present value of an annuity for 5 periods with a fractional exponent $\frac{2}{5}$. - The discount factor $v = (1 + i)^{-1}$ where $i = 0.10$ (10%). - The expression combines these to calculate $P$. 3. **Intermediate calculations:** - Calculate $(1 - 0.25) = 0.75$. - Given $a_5^{\left(\frac{2}{5}\right)} = 3.8833$ (from the problem statement). - Calculate $v^5 = (1.1)^{-5} = 1.1^{-5} \approx 0.62092$. 4. **Evaluate each part:** - First part: $0.75 \times 800 \times 3.8833 = 600 \times 3.8833 = 2330$ (approx $2,330$). - Second part: $10,000 \times 0.62092 = 6,209.2$. 5. **Sum the parts:** $$P = 2,330 + 6,209.2 = 8,539.2$$ 6. **Final answer:** $$P \approx 8,539.19$$ This matches the given result. **Regarding the graph and text alignment:** - The math formulas are enclosed in a rectangular box positioned bottom-right. - The rest of the text is top-left and center aligned. - This layout is not mathematically incorrect; it is a design choice. - The math and text alignment do not affect the correctness of the formulas. Hence, the math is correct and the layout is a stylistic choice, not wrong.