George has been in academia his entire career and wholeheartedly believes that e

Question

George has been in academia his entire career and wholeheartedly believes that education is the key to success. He has two daughters, Cindy and Susie. Cindy is a lingerie and swimsuit model who also believes in education, as well as fashion. Cindy has two children, Red and Mauve, whou are ages 4 and 2 today. She is heading to the hospital at this very moment to deliver her third child, who will be named Olive. Susie is an engineer, who used to play rugby in college and also believes in education. Her children, Cooper and Mercury, are ages 3 and 5 today, respectively. George believes that with $100,000, a student would be able to obtain a great education. George would like to provide each of his grandchildren with the ability to have $100,000 of purchasing power when they turn 18. Education costs are approximately $30,000 per year at private schools and about $15,000 at public schools. Education costs have been increasing at a consistent rate of 7% per year and are expected to continue, while inflation has been at a steady 3% per year. How much should George set aside today to fund his goal for his grandchildren if he can earn a rate of return of 9%?

a. $136,383

b. $179,983

c. $212,444

d. $377,520

Explanation / Answer

First of all we need to find real rate of interest

Real rate of interest = (1+nominal rate of interest)/(1+inflation rate) - 1

=(1.09)/(1.03) - 1

=1.05825-1

=5.825%

Now George has 5 grand child and he wants each of them gets $100,000 when they turn 18

This can be done by finding present value of 100,000$ for each children

PV = FV/(1+r)^n

For Red

PV = 100000/(1.05825)^14

=100,000/2.2092

=45263.71$

For Mauve

PV = 100,000/(1.05825)^16

=100000/2.474

=$40417.703$

For Olive

PV =100,000/(1.05825)^18

=100,000/2.7708

=36090.51$

For Cooper

PV = 100,000/(1.05825)^15

=100,000/2.33797

=42772.1323$

For Mercury

PV = 100,000/(1.05825)^13

=100000/2.08766

=47900.434$

Total amoun to be kept today

=45263.71+40417.703+36090.51+42772.1323+47900.434

=212,444$

Thus ans c. $212,444

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