Parents wish to have \( \$ 150,000 \) available for a child's education. If the child is now 7 years old, how much money must be set aside at \( 4 \% \) compounded semiannually to meet their financial goal when the child is 18 ? Click the icon to view some finance formulas. The amount that should be set aside is \( \$ \square \) (Round up to the nearest dollar.)

To calculate the amount of money that needs to be set aside to reach \$150,000 when the child is 18 years old, we need to find out how many years of investment there are. From age 7 to age 18 is 11 years. Using the formula for compound interest: \[ FV = PV(1 + \frac{r}{n})^{nt} \] Where: - \(FV\) = future value (\$150,000) - \(PV\) = present value (amount to be determined) - \(r\) = annual interest rate (0.04) - \(n\) = number of times interest is compounded per year (2 for semiannual) - \(t\) = number of years until the money is needed (11 years) Rearranging the equation to solve for \(PV\): \[ PV = \frac{FV}{(1 + \frac{r}{n})^{nt}} \] Substituting in the known values: \[ PV = \frac{150,000}{(1 + \frac{0.04}{2})^{2 \times 11}} \] \[ PV = \frac{150,000}{(1 + 0.02)^{22}} \] \[ PV = \frac{150,000}{(1.02)^{22}} \] Calculating \( (1.02)^{22} \): \[ (1.02)^{22} \approx 1.485947 \] Thus, \[ PV \approx \frac{150,000}{1.485947} \approx 100,812.77 \] Rounding up to the nearest dollar, the amount that should be set aside is \( \$100,813 \).