Parents wish to have \( \$ 110,000 \) available for a child's education. If the child is now 4 years old, how much money must be set aside at \( 4 \% \) compounded semiannually to meet their financial goal when the child is 18 ? (i) Click the icon to view some finance formulas.

To find out how much money must be set aside today to reach \( \$ 110,000 \) in 14 years at an interest rate of \( 4\% \) compounded semiannually, we use the formula for compound interest: \[ P = \frac{A}{{(1 + r/n)^{nt}}} \] Where: - \( A = 110,000 \) - \( r = 0.04 \) (annual interest rate) - \( n = 2 \) (number of compounding periods per year) - \( t = 14 \) (time in years) Plugging in the values: \[ P = \frac{110,000}{{(1 + 0.04/2)^{2 \times 14}}} \] Simplifying this gives: \[ P = \frac{110,000}{{(1 + 0.02)^{28}}} = \frac{110,000}{{(1.02)^{28}}} \] Calculating \( (1.02)^{28} \) approximately yields \( 1.747422 \). Thus: \[ P \approx \frac{110,000}{1.747422} \approx 63,000.82 \] So, parents need to set aside approximately \( \$ 63,000.82 \) today. Setting financial goals like education funding can be both exciting and daunting. Knowing what funds you'll need and how compounding interest works gives you the power to make those dreams a reality. Keep in mind that the earlier you start saving, the more time your money has to grow! With investment opportunities and various savings accounts available, it's crucial to explore options that best suit your financial circumstances. Don't hesitate to consult a financial advisor or use online calculators to help you strategize and plan in more detail — every little bit helps when it comes to achieving that financial goal!