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I have a single college fund to be used by 2 children going to college.

Child A is going to college this year and child B in 5 years. I want to give child A 50% of the fund, making sure that child B will have the equivalent of 50% when she goes to college.

Assuming a fund of $100k today, an yearly growth rate of 10%, I can play around with future value in 5 years, and I get $61,693.30 for child A now, because the remainder's future value will end up being the same ($61,693.32).

My question: what is the formula I can use to calculate that 50% amount at any time?

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    Are you going to make more contributions to the fund after Child A starts school?
    – codeMonkey
    Commented Apr 9 at 16:39
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    1) It would be odd to have a college fund that you're starting to draw down invested aggressively enough to expect 10% annual returns. 2) Are you really trying to give both equal dollar amounts? Or equal purchasing power? If they both go to the same school with the same scholarships, $50k today might cover 2.5 years of costs while $50k in 5 years might only cover 1.5 years of costs. If equity is the goal, you'd prefer to cover 2 years of costs for each even if that means giving the younger child more nominal dollars.
    – Justin Cave
    Commented Apr 9 at 19:36
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    Great points, @JustinCave!
    – Gus
    Commented Apr 10 at 4:40
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    There is no single solution that is objectively 'fair' here - there are too many variables and unknowns. The important thing, I suspect, is that A and B feel they have been treated equally. So you may wish to consider involving them in the conversation about how to implement the split.
    – avid
    Commented Apr 10 at 15:32
  • If you have a yearly growth rate of 10% on your investment, you may want to look into having your children take out student loans and then figure out an equitable distribution of the fund after both have graduated.
    – arp
    Commented Apr 12 at 6:38

2 Answers 2

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If you want to remove X now and expect that the remaining (T-X) grows to X in N years at annual rate r, the formula would be:

X = (T-X)(1+r)^N
X + X(1+r)^N = T*(1+r)^N
X(1+ (1+r)^N) = T*(1+r)^N

           (1+r)^N  
X =  T * -----------
          1+(1+r)^N

On the other hand, if you assume (rightly) that college costs will also increase by r over the next 5 years, then it would be perfectly fair to just give child A 50% of the current balance. The other half will grow, and give B a similar benefit relative to the college costs at that time.

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  • I believe the same formula applies even if child A is going to college in M years (and child B in M+N years). (1+r)^M is applied to both X and (the implied) Y so it ends up canceling out.
    – stannius
    Commented Apr 16 at 18:05
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There are 2 Questions hiding in the Post.

(QUESTION 1)
When I have X amount of money , what amount Y of money can I withdraw (& give to Kid1) such that the remaining money X-Y generates interest over 5 years @ 10% to yeild Y ? I want to give that Y to Kid2 , making it look like I gave Equal treatment.

Equation : (X-Y)[1+10/100]^5=Y
X[1+10/100]^5-Y[1+10/100]^5=Y
X[1+10/100]^5=Y+Y[1+10/100]^5
X[1+10/100]^5=Y[1+[1+10/100]^5]
SOLUTION : Y = X[1+10/100]^5 / [1+[1+10/100]^5]
Change the 10 & 5 according to timelines & banking interest.

(QUESTION 2)
Ensuring Equal treatment need not be by the calculation given.

One Simple Solution is to split it up your Bank Account AC0 50%-50% right now.

Slightly Better Solution is to match every withdrawal for Kid1 (towards yearly admission or textbooks or travel or hostel or what-ever or towards Bank Account AC1) with the Equal withdrawal for Kid2 (towards a Dedicated Bank Account AC2)

Your Account AC0 will generate Interest which goes to both kids.
Account AC1 will generate Interest which goes to Kid1.
Account AC2 will generate Interest which goes to Kid2.
At the end of 5 years , Kid2 can starting using AC2.

You have matched the Contributions to the kids Equally , hence given Equal treatment.
You have generated & used Interest amount Equally too.
Assuming AC0 still have some small residual money , you can split it 50%-50% at the end of 5 years.

Numerically , Kid2 will get larger amount , though that is necessary you when you consider rising costs & inflation & such.

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