Time Value Finance Problem

1. A father is now planning a savings program to put his daughter through college. She is 13, she plans to enroll at the university in 5 years, and she should graduate 4 years later. Currently, the annual cost (for everything – food, clothing, tuition, books, transportation and so forth) is $15,000, but these costs are expected to increase by 5% annually. The college requires that this amount be paid at the start of the year. She now has $7,500 in a college savings account that pays 6% annually. Her father will make six equal annual deposits into her account; the first deposit today and the sixth on the day she starts college. How large must each of the six payments be?

Step 1:        Annual cost of college: $15,000 per year at a 5% inflation rate:

        College        Current        Years        Inflation        Cash

        Year        Cost        from Now        Adjustment        Required

        1        $15,000        5        (1.05)5        $19,144.22

        2        15,000        6        (1.05)6        20,101.43

        3        15,000        7        (1.05)7        21,106.51

        4        15,000        8        (1.05)8        22,161.83

Timeline:

        13        14        15        16        17        18        19        20        21