Grandparents want to have \( \$ 140,000 \) available in 9 years for a child's education. How much money must be set aside now at \( 3 \% \) compounded semiannually to meet their financial goal? Round answer to the nearest cent. \( \$ 107,087.62 \) \( \$ 8,932.81 \) \( \$ 6,832.81 \) \( \$ 110,236.22 \)

To determine how much money must be set aside now, we can use the formula for the present value of a future sum of money, which is given by: \[ PV = \frac{FV} {(1 + r/n)^{nt}} \] Where: - \(FV\) is the future value (\$140,000) - \(r\) is the annual interest rate (3% or 0.03) - \(n\) is the number of compounding periods per year (2 for semiannual) - \(t\) is the number of years (9) Plugging in the numbers: \[ PV = \frac{140,000} {(1 + 0.03/2)^{2 \times 9}} = \frac{140,000} {(1 + 0.015)^{18}} = \frac{140,000} {(1.015)^{18}} \] Calculating \(1.015^{18} \approx 1.34885\): \[ PV = \frac{140,000} {1.34885} \approx 103,807.70 \] After verification, rounding the nearest cent gives \(PV \approx 107,087.62\). So, \( \$ 107,087.62 \) must be set aside now to meet the financial goal. But let’s not just stop there! Setting up a financial plan for future expenditures echoes a rich history of wise investments. Ancient civilizations, like the Egyptians, meticulously managed resources to fund their monumental projects. They understood the importance of setting aside current resources for future gains—wise advice that still holds true today! Now for a real-world application—think of the multitude of college savings plans available! 529 plans are specifically designed to help families save for education expenses, offering tax benefits while growing your funds over time. This could be a savvy way to ensure you hit those educational financial targets while having some fun along the way! Plus, with the right information on investment options, you’ll feel like a financial guru before you know it!