Listening to Dave Ramsey on the radio, I heard a woman call in and ask how she might divide up an inheritance among the college funds for her three kids. Dave gave her a good, principled answer, but there is a way that you can go beyond principles and actually calculate what share of the money each kid will need.

Let's say that you inherit $100,000 and you have three kids-- one aged 16, another 14, and another 11. How can you divide up the $100k so that when each of the kids is 18 that they would have about the same amount of money saved for college?

For purposes of illustration, we'll assume that each of the kids' college savings is invested in the same thing and will earn the same rate of return over time. Though if you follow the example below, you'll be able to account for different rates of return for each kid's account.

What we have here is a basic time value of money problem, albeit with some complexity in that there are three interrelated problems.

The first thing we want to do is think in terms of factors, or percentages. That way, it doesn't matter exactly what the lump sump turns out to be, we will now how to divide it proportionally to get what we want.

Then we need to introduce the element of time. We need to figure out how much INequality we need to do to account for the different amounts of time. How do we allocate a total based on the different times available for the kids' college funds to grow? How much do we discount the pre-growth values so the values end up being the same?

We can use a basic time value equation to solve for the discounted factor for each. Let's take the 16 years old as an example. His savings will only have two years to grow. If we assume 8% per year (a reasonable assumption over the long term, less so in the short term), we can solve. N is the number of periods (years before they go to college):

FV=PV(1+r)^n

FV=PV (1.08^2)

FV=PV* 1.1664

PV= FV * 0.8573, or 85.7%

The 16 year old kid needs about 85.7% of what his 18 year-old self will need to go to college. That makes sense.

We repeat for the 14 year old Kid:

FV=PV(1.08^4)

FV=PV(1.36)

PV=FV(0.735).

The 14 year old will need to have 73.5% of what is 18 year-old self will need to go to college.

Finally, the 11-year old:

FV=PV(1.08^7)

FV=PV(1.7138)

PV=FV(0.5835)

The 11-year old kid needs to have 58.35% of his total college expenses in savings to he'll have 100% at age 18.

So we now know the relative weightings for the three kids: 85.7%, 73.5%, and 58.35%

How do we translate that into a proportion for allocation of a lump sum?

To weight them, we can first just add them all together in decimal versions to get a total of 2.18. Then we take each kid's factor divided by the total to normalize it

16YO: 0.857/2.18= 0.391, or 39.1%

14YO: 0.735/2.18= 0.337 or 33.7%

11 YO: 0.5835/2.18= 0.268 or 26.8%

To make sure each kid has roughly 33% of all the windfall, we need to allocate the percentages as above.

Let's check out work to see if this makes sense for a windfall of $100k.

The allocation says we should allocate to the 11 year old $26,800 in a college fund. Left to grow at 8% for 7 years, this amount becomes $45,931 at age 18.

What do we get if we allocate $33,700 to the 14 year old and let it grow for four years? $45,848

The 16 year old will have $45,606 saved for college in two years.

Now there's some rounding error (magnified by repeated rounding) that produces a couple hundred dollars variance between the three kids, but this should suffice to illustrate how you can account for the different ages of children in allocating a windfall towards college savings.

Hope this helps!

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