Explain how you reached the answer or show your work if a mathematical calculation is needed, or both. 5. 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 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, 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? a. $1,965.21 b. $2,068.64 c. $2,177.51 d. $2,292.12 e. $2,412.76
Current college costs $14,500
College cost inflation 3.5%
Account return 9.0%
First 4 payments $5,000
Current account balance $15,000
First, determine each year of college\'s costs.
Year 1 of college (t = 8) = 19,093.73
Year 2 of college (t = 9) = 19,762.01
Year 3 of college (t = 10) = 20,453.68
Year 4 of college (t = 11) = 21,169.56
The PV (at t = 8) of all college costs is: 70,786.26. This is what they need at t = 8.
After the first 4 payments, the college account will have (at t = 3): $42,291.08
5 more contributions are left in order to get the required funds for college costs.
N 5
I 9.0%
PV $42,291
FV $70,786.26
PMT $955.13
Step 1. Calculate the purchasing power of $2,500,000 in 35 years at an inflation rate of 2%:
N 35
I/YR 2.0%
PMT $0.00
FV $2,500,000
PV $1,250,069.03
Step 2. Calculate the real rate on the growing annuity:
rNOM 9.0%
Inflation 2.0%
rr = [(1 + rNOM)/ (1 + Inflation)]
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