You have an absolutely brilliant child who is six years old and will be attending a private college in twelve years. You know that in twelve years a four -year college will cost at least $70,000 per year (total $280,000), including tuition, books, and room and board. You determine that you can earn 12 percent on a mutual fund investment during the next twelve years, and invest at the end of each year. How much will your total investment be for the twelve -year period?

Question

Quizplus · Accepted Answer

To solve this, we use the future value of an annuity formula: FV = P * [((1 + r)^n - 1) / r], where FV is the future value ($280,000), P is the annual payment, r is the annual interest rate (12% or 0.12), and n is the number of periods (12 years). Rearranging the formula to solve for P gives us P = FV / [((1 + r)^n - 1) / r]. Plugging in the values gives us P = $280,000 / [((1 + 0.12)^12 - 1) / 0.12], which calculates to approximately $139,227.

You Have an Absolutely Brilliant Child Who Is Six Years