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,including tuition,books,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

The correct answer is A because the total investment will be $139,227. This is calculated by taking the present value of the future cost of college, which is $70,000 per year for four years, and then multiplying that by the factor (1 + r)^n, where r is the annual interest rate and n is the number of years. In this case, r = 0.12 and n = 12, so the factor is (1 + 0.12)^12 = 3.386. Therefore, the present value of the future cost of college is $70,000 * 3.386 = $237,020. To find the total investment, we divide the present value by the factor (1 + r)^n - 1, which is (1 + 0.12)^12 - 1 = 2.386. Therefore, the total investment is $237,020 / 2.386 = $139,227.

You Have an Absolutely Brilliant Child Who Is Six Years