Parents wish to have $ 150 comma 000 available for a child's education. If the child is now 10 years old, how much money must be set aside at 7 % compounded semiannually to meet their financial goal when the child is 18?
To calculate the amount that must be set aside, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Total amount needed ($150,000)
P = Principal amount (amount to be set aside)
r = Annual interest rate (7%)
n = Number of times interest is compounded per year (2 for semiannual)
t = Number of years the money will be invested (8 years for the child to turn 18)
Plugging in the values, we get:
$150,000 = P(1 + 0.07/2)^(2*8)
$150,000 = P(1 + 0.035)^16
$150,000 = P(1.035)^16
$150,000 = P(1.7675)
P = $150,000 / 1.7675
P ≈ $84,838.59
Therefore, the parents must set aside approximately $84,838.59 at 7% compounded semiannually to have $150,000 available for the child's education when they turn 18.