Question

Let’s assume that you’re preparing for your (future) child (or grandchild)’s college education. 20 years later from now, your (future) child will go to college. Currently, you’re considering two colleges for your (future) child (or grandchild)

University 1 Harvard University

University 2 Vanderbilt University

1. Please visit the website of each university and find tuition and related information. Use out-of-state tuition information. Make sure that you include accurate information and citation source (20 points).

2. Using the tuition and related information in (1), you need to compound it at a reasonable "inflation" rate for education-related expenses for x number of years. I hope most of you are aware that educational inflation has been much higher than overall inflation in the economy, (You can find ‘tuition inflation’ statistics from the internet. Use google.com and search for tuition inflation or education inflation) (20 points).

3. After you calculate this projected cost, your next job is to find the annual deposit needed to accomplish the goal - meeting the educational expenses. You must assume the investment rate of return (You can use ‘savings account rate as your investment rate of return, for example). Recall the equations or time value of the money table we went over in class. You will choose the one that will give you the amount of the annual deposit (20 points).

4. What if you have $10,000 right now? How does this new information affect the previous answer in (3)? What’s new annual deposit amount you should make? (20 points)

5. Let’s assume that you just won the lottery. Rather than making equal annual payments, you decided to make one lump-sum deposit today to cover your child’s future college expense needs. There will be no additional deposit. How much should you make one lump-sum deposit today to accumulate projected college education expense you need in 20 years? (20 points)

Answer 1

(1) The estimated cost of tuition in University of Harvard for 2019-2020 is $66,700

The estimated cost of tuition in University of  Vanderbilt for 2019-2020 is $74,193

(2) The 10-year historical rate of education inflation is approximately 5 percent.

To calculate the estimated tuition fee 20 years from now, we need to compound the current tuition fee at the appropriate interest rate for 20 years. The appropriate rate to use here is the 10-year historical education inflation rate, which is 5%.

FV = PV * (1 + r)^n,

where FV = future value

PV = present value

r = rate of interest

n = number of years

Projected cost of tuition 20 years from now :

Harvard : $66,700 * (1 + 0.05)^20, which is $176,975

Vanderbilt : $74,193 * (1 + 0.05)^20, which is $196,856

(3) To find the annual deposit, we use the PMT function in Excel.

rate = savings accounts rate, which is around 2.25%

nper = number of years over which the annual deposit is to be made, which is 20 years

pv = zero as the initial savings are zero

fv = projected cost of tuition

Harvard=PMT(0.0225,20,0,176975) , which is $7,104.14

Vanderbilt =PMT(0.0225,20,0,196856), which is $7,902.21

(4) If you have $10,000 right now, we use the same formula with this change :

pv = -10000 as this is the initial savings. We use the negative sign as we used a positive sign for the FV.

Harvard =PMT(0.0225,20,-10000,176975), which is $6,477.72

Vanderbilt =PMT(0.0225,20,-10000,196856), which is $7,275.79

(5) This is a future value problem. Let the lump-sum deposit be X

X compounded at 2.25% for 20 years should equal the projected tuition fee

Harvard : $176,975 = X * (1+ 0.0225)^20

X = $113,408.47

Vanderbilt : $196,856 = X * (1 + 0.0225)^20

X = $126,148.64