Question

1) You have two children who will be going to college. The first child will begin 17 years from today, and tuition will be $20,000, $21,000, $22,000 and $23,000 at t=17, 18, 19, and 20. The second will begin college 19 years from today, and tuition will be $22,000, $23,000, $24,000 and $25,000 at t=19, 20, 21, and 22.

a) To fund your children’s tuition, you would like to make an equal annual deposit over the next 20 years (first deposit at t=1, last at t=20) in an account earning 4% per year, compounded semi-annually. What equal amount must you deposit each year?

b) What if (instead of an equal annual deposit) to fund your children’s tuition you plan to make deposits over the next 20 years (first deposit at t=1, last at t= 20) that grow each year by 3%. If those deposits earn 4% per year, compounded semi-annually, what is the amount of the first deposit (at t=1)?

c) Good news! Your parents have offered to pay the entire college tuitions of your children. They plan to do this by making a single deposit 5 years from today (at t=5). If invested funds earns 4% per year, compounded semi-annually, what single amount should they deposit?

Answer 1

The logic of all the answers is to ensure that the value of the deposited amount at the end is equal to the required amount of tuition fees. As the total period of the question is 22 years, the tuition fees required at the end of the t=17, t=18......are all made to grow at 4% compounded semi-annually till the end of 22 years to arrive at the single value of tuition fees required.

Similarly, annual deposits are also made to grow (as per the question) until the end of 22 years and is equated to the required annual tuition fees.

a) Amont aloposit of - uual annual a (at t=1). This & becomes xn1.02² every sube quit year. : it becomes a x1-02) 4 at the end of year 22. For 20, such installments, the 2 tallment Similarly the requind amount is 20,000 (1.022" + 21000 (02")" - 44000 x (1.0243 . 46.000 (024² + 24, 0b0 x .02 + 25. On solving. (x = 6631.57

Dare to challenge the status quo and try new things b) Annual t=1 i This grow deposit at xi each year by The amount deposited next year i x*1.03. Hence, The deposity and the tuition fees ghould be equal at the end of year value of deposits at t=22 xx11.0242 + x x103 x (1.022 20 + x x (h0 22 34x633) + + ** 4:03) X(102) - 20,00 (0.02%) 't nito xl.02415 + uues vbn"), 45, (102) + 24,600 X-02 + 25,000 Aet with integrity Make a difference Workingether

16 continue On solving, la = 5130.99

Amount deposited at t -5 is x . each The year amount as will grow xx/1.04) 12 Because 4% compounded semi-annually Amount required for tuition rus t ... 17 18 19 20 21 22 Son 1 (in 'soo) 20 21 22 23 Son 2 (in anl 2 2 23 24 25 Totoy 20 21 44 46 24 - 44 46 24 25 TU # The investment has to be equal to tuition fees at en of year 22 it tuition & Hus required at t=17, t - 18 t=19 . also grow @ 4.%. Compounded uni- annually.

D ③ Continue Innovate, test and learn from failure e Incest met year 5 = year 6 = x xx (102) Therefore at end of year 22 2 x (102)* *(1-02)) = 20,00 d(102) 13 ASAL + [ 44,00 x (102) + [ 46,00 x (1 0277 + [ 24,80 x (voz) e 25,000 24,000 x La On solning, x = 101,137.24