College tuition is 6000 for the current school year, payable in full at the beginning of the school year. College tuition will grow at an annual rate of 5%. A parent sets up a college savings fund earning interest at an annual effective rate of 7%. The parent deposits 750 at the beginning of each school year for 18 years, with the first deposit made at the beginning of the current school year. Immediately following the 18th deposit, the parent pays tuition for the 18th school year from the fund. The amount of money needed, in addition to the balance in the fund, to pay tuition at the beginning of the 19 th school year is X.

Calculate X.

• 1439
• 1545
• 1664
• 1785
• 1870

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: E

At the time of the final deposit the fund has

[[math]]750 s_{\overline{18}|0.07} = 25, 499.27[[/math]]

This is an immediate annuity because the evaluation is done at the time the last payments is made (which is the end of the final year). A tuition payment of 6000 (1.05)¹⁷ = 13, 752.11 is made, leaving 11,747.16. It earns 7%, so a year later the fund has 11,747.16(1.07) = 12,569.46. Tuition has grown to 13,752.11(1.05) = 14,439.72. The amount needed is 14,439.72 – 12,569.46 = 1,870.26

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.