Parents wish to have \( \$ 130,000 \) available for a child's education. If the child is now 8 years old, how much money must be set aside at \( 3 \% \) compounded semiannually to meet their financial goal when the child is 18 ? (i) Click the icon to view some finance formulas. The amount that should be set aside is \( \$ \square \). (Round up to the nearest dollar.)

To determine how much money parents need to set aside now to have \$130,000 available for their child's education in 10 years (when the child turns 18), we'll use the **Present Value (PV)** formula for compound interest. ### Given: - **Future Value (FV)**: \$130,000 - **Annual Interest Rate (r)**: 3% or 0.03 - **Compounding Periods per Year (n)**: 2 (since it's compounded semiannually) - **Time (t)**: 10 years ### Formula: The present value \( PV \) is calculated using the formula: \[ PV = \frac{FV}{\left(1 + \frac{r}{n}\right)^{nt}} \] ### Plugging in the Values: \[ PV = \frac{130{,}000}{\left(1 + \frac{0.03}{2}\right)^{2 \times 10}} \] \[ PV = \frac{130{,}000}{\left(1 + 0.015\right)^{20}} \] \[ PV = \frac{130{,}000}{(1.015)^{20}} \] ### Calculating \((1.015)^{20}\): \[ (1.015)^{20} \approx 1.346855 \] ### Final Calculation: \[ PV = \frac{130{,}000}{1.346855} \approx 96{,}448.18 \] ### Rounding Up: Since we need to round up to the nearest dollar: \[ PV \approx \$96{,}449 \] ### **Answer:** The amount that should be set aside is **\$96,449**.