Scott and Linda have been saving to pay for their daughter Casie\'s college educ
ID: 2739045 • Letter: S
Question
Scott and Linda have been saving to pay for their daughter Casie's college education. Casie 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 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, 10, and 11).
So far, Scott and Linda 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 Casie's anticipated college costs?
a.
$1,965.21
b.
$2,068.64
c.
$2,177.51
d.
$2,292.12
e.
$2,412.76
a.
$1,965.21
b.
$2,068.64
c.
$2,177.51
d.
$2,292.12
e.
$2,412.76
Explanation / Answer
Answer: Option (e) $2,412.76
1) Amount needed at the end of the 8th year:
2) Amount to be contributed at the end of the 5th, 6th and 7th year:
70786.26 should be the sum of
$8620.88 = A*fvifa(9,3)*1.09, where A is the equal amounts to be deposited at the end of years 5 to 7.
Therefore, 8620.88 = A*3.2781*1.09 and A = $2,629.84 = $2,412.70
This is very close to Option (e)
year 8 year 9 year 10 year 11 tution fee required 19093.73 19762.01 20453.68 21169.56 pvif @ 9% 1.0000 0.9174 0.8417 0.7722 PV at the end of the 8th year 19093.73 18130.29 17215.45 16346.79 Amount required at the end of the 8th year = 70786.26Related Questions
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