John and Daphne are saving for their daughter Ellen\'s college education. Ellen

Question

John and Daphne are saving for their daughter Ellen's college education. Ellen just turned 10 (at t = 0), and she will be entering college 8 years from now (at t = 8). College tuition and expenses at State U. are currently $14,500 a year, but they are expected to increase at a rate of 3.5% a year. Ellen should graduate in 4 years¾if she takes longer or wants to go to graduate school, she will be on her own. Tuition and other costs will be due at the beginning of each school year (at t = 8, 9, 10, and 11).

So far, John and Daphne have accumulated $15,000 in their college savings account (at t = 0). Their long-run financial plan is to add an additional $5,000 in each of the next 4 years (at t = 1, 2, 3, and 4). Then they plan to make 3 equal annual contributions in each of the following years, t = 5, 6, and 7. They expect their investment account to earn 9%. How large must the annual payments at t = 5, 6, and 7 be to cover Ellen's anticipated college costs?

$2,292.12

$2,412.76

$2,177.51

$2,068.64

$1,965.21

a.

$2,292.12

b.

$2,412.76

c.

$2,177.51

d.

$2,068.64

e.

$1,965.21

Explanation / Answer

We first need to compute the amount required for tuition expenses each year from year 8 to 11.

FV= PV x (1+r)^n

Year

today's expense

FV factor 3.50%

Fv

8

14500

1.3168

19093.73

9

14500

1.3629

19762.01

10

14500

1.4106

20453.68

11

14500

1.4600

21169.56

Amount of money required at year 7 would be

Year

cash flow

PV factor at year 7 at 9%

PV

8

$19,093.73

0.9174

$17,517.18

9

$19,762.01

0.8417

$16,633.29

10

$20,453.68

0.7722

$15,794.00

11

$21,169.56

0.7084

$14,997.05

$64,941.52

FV of current investment = pmt x PVIF(3,9%) + PV x FVIF(4, 9%)

                                                = 5000 x4.573129 + 15000 x 1.41158

                                                = 44,039.37

Now we need to accumulate $64,941.52 in next three years.

FV of current investment = pmt x PVIF(3,9%) + PV x FVIF(3, 9%)

                $64,941.52           = Pmt x3.2781 + 44,039.37 x 1.295029

                                                Pmt = (64,941.52 – 57032.26129)/3.2781

                                                Pmt =2412.76

Option B is correct

Year

today's expense

FV factor 3.50%

Fv

8

14500

1.3168

19093.73

9

14500

1.3629

19762.01

10

14500

1.4106

20453.68

11

14500

1.4600

21169.56

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