A father, concerned about the rapidly rising cost of a college education, is pla

Question

A father, concerned about the rapidly rising cost of a college education, is planning a savings program to put his daughter through college. She is 12 years old, plans to enroll at the university 6 years from now, and should take 4 years to complete her education. Currently, the cost per year (for everything-food, clothing, tuition, books, transportation, and so forth) is $12,000, but an 8 percent annual inflation rate in these costs is forecasted. The father's bank account pays 4 percent interest rate, compounded annually. How much will the father have to save each year before the time his daughter starts college in order to put her through school? (Note: The first deposit occurs one year from today, and the last deposit occurs when his daughter attends college at the age of 18. In total, there are six annual installment deposits.)

Please show work and explain what steps you took

Explanation / Answer

Expected 1st installment of college fee = $12,000 * (1 + 5%)8

= $12,000 *1.586874= $19,042.49

PV of the college fees for next 4 years = $19,042.49 + $19,042.49 * (1 + 8%) / (1 +4%) + 19,042.49 * (1 + 8%)2 / (1 +4%)2 + $19,042.49 * (1 + 8%)3 / (1 +4%)3

= $80,678.15

Again,

$80,678.15 = Annual deposit * [(1 + 4%)8 - 1] / 4%

$80,678.15 = Annual deposit * 9.214226

Annual deposit = $8755.86

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