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Saving for college tuition using the time-value of money

Let's use the time-value of money to determine how much you need to save for your child's college tuition.

Many of us know what it feels like to be burdened with college and/or professional school debt. Some of us don’t want our children to be burdened with the same hurdle, and thus we’re committed to funding our child’s secondary schooling.

How much must we save in order to fund our child’s secondary schooling? Let’s look at a specific example and quantitatively walk through the finances:

Fully fund your single child’s 4-year secondary schooling,
Freshman year starts 17 years from today,
Freshman year tuition: $40,000 (I know…what planet am I living on?!?!?!),
Tuition grows 5% every year, and
Assume an 8% required rate of return

Let’s review some of the assumptions above, so you understand where these numbers originated (in reverse order).

8% required rate of return

This value is the average that we see over a period of time. The table shows the average rates of return over 5-, 10-, 20-, and 30-year periods:

Source: https://www.macrotrends.net/2526/sp-500-historical-annual-returns

Since our kiddo will be going to school in 17 years, I used the 20-year average rate of return (7.64% → rounded up to 8%).

5% annual tuition growth rate

We assumed a 5% growth rate in your child’s tuition each year, and we assumed the traditional 4-year schooling career. Here’s where we get the 5% tuition growth rate:

Source: National Center of Educational Statistics

$40,000 freshman year tuition, 17 years from today

I’m writing this tutorial in calendar year 2023. Seventeen years from now would be the year 2040. Here’s the projected cost of tuition for college.

Source: Massachusetts Educational Financing Authority

I assumed that you’d be sending little Jane/Johnny to a 4-year, in-state school: $39,582.40 → $40K rounded up.

Now we’re ready to look at the annual tuition for junior. At a 5% annual growth rate, here is what you’re facing.

The untrained eye would look at the annual tuition and arithmetically add the values to obtain the total amount needed. That is, $40,000 + $42,000 + $44,100 + $46,305 = $172,405. This value is the *accounting cost* that you will see in your bank account. It isn’t the true, *economic* value that you need to save.

Accounting versus Economic value

Let’s review the difference between an *accounting value* and an *economic value*. Below are the accounting and economic values of the 4 years of tuition that you want to fund.

Why are these values unequal? The accounting value does not take into account the *time value of money*. Remember:

$1.00 today (t = 0) ≠ $1.00 tomorrow (t = 1).

Simply adding $1.00 (t = 0) with $1.00 (t = 1) gives you:

an accounting value of $2.00, but
an economic value of $1.93.

Determining economic value

How do you calculate the *economic value* of the cost of 4 years of college? You discount each tuition amount by the:

appropriate required rate of return (which is 8%: see above if you forgot how I got this number), and
appropriate discounting period
1. Freshman year: discounting period = 0
2. Sophomore year: discounting period = 1
3. Junior year: discounting period = 2
4. Senior year: discounting period = 3

Discount the tuition back to freshman year (t = 17) so that you can arithmetically add all the tuition values. The total cost of 4-years of college, beginning at t = 17 and considering an 8% required rate of return (i.e., the time value of money) = $40,000 + $38,889 + $37,809 + $36,758 = $153,456.

Your task with the help of TVM

You need to have $153,456 ready for deployment at t = 17 (17 years from today). How in the world are you going to manage that task!?!?!?!

Thankfully, you can use the time value of money (TVM) to help you out in the intervening 16 years that you have before your child leaves the nest.

How much do you need to save, and over what fixed period of time, in order to reach $153,456 at t = 17? Realize a few things:

You’re going to save the exact same amount during each period from 1 to 16
You’re going to grow your money at the same required rate of return…8%
All that compounding is going to help you reach $153,456 by t = 17.

Shown below is the annual amount of savings you must make in order to reach your goal at t = 17.

The amount you “invest” (save) is always the same: $5,060 yearly, or $422 monthly. The compounded value is the interest you earn (8% on average) on the amount you’ve already saved. The more you save in the earlier periods, the more compounding “help” you get and the quicker/easier it is to reach $153,456.

Sensitivity analysis - brief

Say you decide to save $522 monthly → $6264 annually. When would you reach $153,456? Somewhere between periods 14 and 15.

Save an extra $100 per month, and you’ll have junior’s college fund 2-3 years ahead of freshman year.

Reach out for questions.

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