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). The following is the list of universities I assigned to each of you.

Student University 1 University 2

Holliday, Carshawn B	Harvard University	Vanderbilt University

Estimate future costs of two colleges for your (future) child (or grandchild) and calculate needed annual savings for two colleges. Please specify your assumptions for computation of future costs and needed annual savings.

1.       Please visit 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.

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).

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 money table we went over in class. You will choose the one that will give you the amount of the annual deposit.

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

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?

Answer 1

Harvard University

Part 1

Based on the website of Harvard University, the total cost of attending Harvard College without financial aid in 2018-2019 is $ 67,580. This includes for tuition, room, board, and fees combined.

Source: "Harvard at a Glance", retrieved from https://www.harvard.edu/about-harvard/harvard-glance on February 06, 2019

This is the annual fees. Hence the total fees for four years graduate program = 4 x $ 67,580 = $ 270,320

Part 2

Annual Rate of Increase in Tuition and Fees for four years program = 3.9%

Source: "Tuition Inflation", retrieved from https://www.edvisors.com/plan-for-college/saving-for-college/tuition-inflation/ on February 06, 2019

Hence, the inflation adjusted cost = kitty size required 20 years from now = $ 135,160 x (1 + 3.9%)²⁰ = $ 581,017

Part 3

Let's say we need an annual deposit of A. Reinvestment Rate, R (assumed) = 2.25% = 0.0225

Source: "Best Savings Rates February 2019", retrieved from https://www.nerdwallet.com/blog/banking/best-savings-rates/ on February 06, 2019

Hence, the future value of this annuity over N = 20 years at R = 2.25% must equal to the kitty size required 20 years from now.

Hence, (A / R) x [1 - (1 + R)^-N] = $ 581,017

Hence, A / 0.0225 x [1 - 1.0225^(-20)] =15.96 x A = $ 581,017. Hence, A = $ 36,396

Part 4

If you have $10,000 right now, it's future value at the end of 20 years from now = $ 10,000 x (1 + R)^N = 10,000 x 1.0225²⁰ = $15,605

A part of the kitty size required, will be met by this.

Balance size of the kitty that needs to be made by annual deposits = $ 581,017 - $ 15,605 = $ 565,412  

The equation to solve now will be: 15.96 x A = $ 565,412  ; Hence, A = $ 26,176.

Hence, the new annual deposit amount, A = $ 35,419

Part 5

Let's say the lumpsum amount required today is "L"

Hence, its future value = size of the kitty required

Hence, L x (1 + R)^N = $ 581,017

Hence, L x (1.0225)²⁰ = 1.56L = 581,017

Hence, L = $ 372,326

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Vandebilt University

Part 1

1. Tuition & Fees: $ 49,810
2. On Campus Room & Board, Other Expenses: $ 19,144
3. Total annual fees = $ 68,954

Source: "Paying for Vanderbilt University", retrieved from https://www.collegetuitioncompare.com/edu/221999/vanderbilt-university/tuition/ on February 06, 2019

This is the annual fees. Hence the total fees for four years program = 4 x $ 68,954 = $ 275,816

Part 2

Annual Rate of Increase in Tuition and Fees for four years program = 3.9%

Source: "Tuition Inflation", retrieved from https://www.edvisors.com/plan-for-college/saving-for-college/tuition-inflation/ on February 06, 2019

Hence, the inflation adjusted cost = kitty size required 20 years from now = $ 275,816 x (1 + 3.9%)²⁰ = $ 592,830

Let's say we need an annual deposit of A. Reinvestment Rate, R (assumed) = 2.25% = 0.0225

Source: "Best Savings Rates February 2019", retrieved from https://www.nerdwallet.com/blog/banking/best-savings-rates/ on February 06, 2019

Hence, the future value of this annuity over N = 20 years at R = 2.25% must equal to the kitty size required 20 years from now.

Hence, (A / R) x [1 - (1 + R)^-N] = $ 592,830

Hence, A / 0.0225 x [1 - 1.0225^(-20)] =15.96 x A = $ 592,830. Hence, A = $ 37,136

Part 4

If you have $10,000 right now, it's future value at the end of 20 years from now = $ 10,000 x (1 + R)^N = 10,000 x 1.0225²⁰ = $15,605

A part of the kitty size required, will be met by this.

Balance size of the kitty that needs to be made by annual deposits = $ 592,830 - $ 15,605 = $ 577,225

The equation to solve now will be: 15.96 x A = $ 577,225; Hence, A = $ 36,159

Hence, the new annual deposit amount, A = $ 36,159

Part 5

Let's say the lumpsum amount required today is "L"

Hence, its future value = size of the kitty required

Hence, L x (1 + R)^N = $ 592,830

Hence, L x (1.0225)²⁰ = 1.56L = $ 592,830

Hence, L = $ 379,895