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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?

Gus
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2 Answers2

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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.

D Stanley
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2

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.

Prem
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