John and Daphne are saving for their daughter Ellen\'s college education. Ellen
ID: 2662783 • Letter: J
Question
John and Daphne are saving for their daughter Ellen's college education. Ellen is now 10 years old and will be entering college 8 years from now (t = 8). College tuition and expenses at State U are currently $14500 a year, but they are expected to increase at a rate of 3.5% a year. They expect Ellen to graduate in 4 years. (If Ellen wants to go to graduate shcool, she will be on her own). Tuition & other costs will be due at the begining of each school year (at t = 8,9,10, and 11). So far, John and Daphne have accumulated $15000 in the college savings account. Their long term financial plan is to ass an additional $5000 at the begining of each of the next 4 years (at t = 0,1,2 and 3). Then they plan to make 4 equal annual contributions at the end of each of the following 5 years (t = 4,5,6,7 and 8). They expect their investment account to earn 9%. How large must the annual payments be at t= 4,5,6,7 and 8 to meet Ellen's anticipated college costs?Explanation / Answer
Answer: d
Explanation:
they need for studying:
14 500 * ((1.035)^8) + 14 500 * ((1.035)^9) + 14 500 * ((1.035)^10) + 14 500 * ((1.035)^11) = 80 479
Tuition the beginning of t=8: 14 500 * ((1.035)^7) = 18 448.05
Tuition the beginning of t=9: 14 500 * ((1.035)^8) = 19 093.73
Tuition the beginning of t=10: 14 500 * ((1.035)^9) = 19 762.01
Tuition the beginning of t=11: 14 500 * ((1.035)^10) = 20 453.68
Before the studying begins:
from accumulations they have: 1 500 * 1.09^7 = 27 420.59
from regular additions: 5 000 * 1.09^7 + 5 000 * 1.09^6 + 5 000 * 1.09^5 + 5 000 * 1.09^4 = 32 276.7
Total = 59 697.3
Cash flows during studying:
t
we have
tuition
left (year's beginning)
result ((year's end)*1.09)
8
59697,31
18448,05
41249,26
44961,6934
9
44961,69
19093,73
25867,963
28196,07967
10
27196,08
19762,01
7434,07
8103,1363
11
8103,136
20453,68
-12350,5437
So we have to save 9 536.8858 additionally before the study begins (12 350.5437/(1,09^3)) by 3 equal contributions: X*(1,09^3) + X*(1,09^2) + X*1,09 = 9 536.8858, X = 2 292.12
t
we have
tuition
left (year's beginning)
result ((year's end)*1.09)
8
59697,31
18448,05
41249,26
44961,6934
9
44961,69
19093,73
25867,963
28196,07967
10
27196,08
19762,01
7434,07
8103,1363
11
8103,136
20453,68
-12350,5437
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