Final answer:
To reach a total investment of $280,000 for college fees in twelve years, with a 12 percent annual return, the parent should invest $11,836.73 at the beginning of each year.
Step-by-step explanation:
To solve this financial problem, we can use the formula for the future value of an annuity due, as the parent will be investing at the beginning of each year. The formula to calculate the amount to invest annually is P = FV / [{((1 + r)ⁿ) - 1} / r * (1 + r)], where P is the payment (amount to invest annually), FV is the future value desired ($280,000), r is the interest rate per period (12%, or 0.12), and n is the number of periods (12 years). By plugging in the values, we can calculate the annual investment required to meet the future college expenses.
First, we calculate the part of the formula that affects the compound interest:
{((1 + 0.12)¹²) - 1} / 0.12 * (1 + 0.12) = (3.896 - 1) / 0.12 * 1.12 = 23.6667
Now, we divide the future value by this result to find the annual investment needed:
$280,000 / 23.6667 = $11,836.73
Therefore, the parent should invest $11,836.73 annually at the beginning of each year to reach the total investment required for the college fees in twelve years, assuming a 12 percent return on investment.