Saving for the tuition

A. (10 points) Suppose you want to save the same (constant) amount each year in nominal dollars. How much will you have to save each year so that there is enough money to send your child to college?

Tuition increase=3.9%
Tuition price in July 2013= $ 36,993
Tuition in 2032= $36,993 * (1.039)^19 =$76527.05
Tuition in 2033=$36,993 * (1.039)^20 = $79511.6
Tuition in 2034=$36,993 * (1.039)^21=$82612.55
Tuition in 2035=$36,993 * (1.039)^22=$85834.44

Various tuitions Discounted in 2031 : Nominal savings interest is 7.5 % (our best alternative)
Tuition in 2032= 76527.05/(1.075)= $71187.95
Tuition in 2033= 79511.6/(1.075)^2=$68803.98
Tuition in 2034=82612.55/(1.075)^3=$66499.85
Tuition in 2035=85834.44/(1.075)^4=$64272.88
Total Money needed in savings account in 2031 =$270764.66
Now , using my HP 12 C :
N=18 i=7.5% PV=0 FV=$270764.66 PMT = ??
PMT = $7589.25 (Answer)

B. (10 points) In the first part of this problem, you calculated the constant nominal amount saved each year. Of course, in real terms, the value of these amounts gets less and less over time due to inflation. Suppose instead that you want to save the same (constant) amount each year in real dollars. How much will you have to save each year so that there is enough money to send your child to college? In addition, provide the corresponding (increasing) cash flows saved in nominal dollars made each year.

Nominal Savings Rate= 7.500%
Total Money needed in savings account in 2031 =$270764.66
Real interest rate= [(1+0.075)/(1+0.019)^----1] =5.497%
PV =[$270,764.66 /(1+0.075)^18 ] = $73,661.34
N=18
Solving for PMT we get $6547.74.This is the real dollar value.

Change in future cash flows if the rate of inflation is 1.9 %:

Year Payment Year Payment Year Payment
1 $6,547.74 7 $7,330.55 13 $8,206.95
2 $6,672.15 8 $7,469.83 14 $8,362.88
3 $6,798.92 9