Nathan and Nicole are saving for their daughter Jessica\'s college education. Je
ID: 2696935 • Letter: N
Question
Nathan and Nicole are saving for their daughter Jessica's college education. Jessica just turned 10at (t=0), and she will be entering college 8 years from now (at t=8). College tuition and expenses at State University are currently $14,500 a year, but they are expected to increase at a rate of 3.5% a year. Jessica should graduate in 4 years, if 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=8,9,10and11). So far, Nathan and Nicole 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 Jessica's anticipated college costs?Explanation / Answer
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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