To calculate the amount of money that needs to be set aside at 4% compounded semiannually to reach a goal of $140,000 by the time the child is 18, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future amount (goal of $140,000)
P = the principal amount (the amount to be set aside)
r = the annual interest rate (4% or 0.04)
n = the number of times the interest is compounded per year (semiannually, so n = 2)
t = the number of years (18 - 7 = 11 years)
Plugging in the values into the formula, we have:
$140,000 = P(1 + 0.04/2)^(2*11)
Simplifying further:
$140,000 = P(1.02)^22
Now, we can solve for P:
P = $140,000 / (1.02)^22
Using a calculator, we find:
P ≈ $95,113.16
Therefore, approximately $95,113.16 must be set aside at 4% compounded semiannually to reach the financial goal of $140,000 by the time the child is 18 years old.