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College Funding Math – Part 3

By JLP | February 21, 2006

A big thanks goes out of the Unknown Professor (UP – pretty cool initials), who writes for the FinancialRounds blog, for helping me with the math on this one. It is one thing to use a program to solve problems. It is quite another to solve problems using the actual formulas. UP came through for me and I really appreciate it.

In Part I of this series, I showed you how to use a formula to figure out how much your future college funding needs could be, using today’s college tuition prices and an assumed inflation rate.

I followed up with Part II by showing you how to calculate how much you need now in order to meet those future needs. We discovered that a lump sum of $31,580, invested to get an 8% return, would fund four years of college for Hector.

The obvious problem with the lump sum is that there aren’t a lot of people with $30,000 available to invest for college. So, in this post, it is my aim to show you how to calculate how much you need to save each year in order to meet Hector’s college funding needs.

NOTE: I must warn you that the formula used to perform this calculation looks like something out of a scary movie. But, if you take it one step at a time, it really isn’t that bad. I promise.

We are trying to figure out how much we have to save each year to meet a goal. The amount saved each year is called a “payment.” So, we need to use a formula to calculate a payment. This formula involves two steps. First, we have to solve for the factor (or constant). Then we use the factor to solve for the payment.

The first formula looks like this:

[((1 + i)n – 1) ÷ (i X (1+ i)n] X (1 + i)

i = interest rate or rate of return expected, which is 8% or .08.
n = number of years, which is 17
X = multiplication sign

Once we add in the appropriate numbers, the forumula* looks like this:

[((1 + .08)17 – 1) ÷ (.08 X (1+ .08)17] X (1 + .08)

[((1.08)17 – 1) ÷ (.08 X (1.08)17] X 1.08

[(3.7000181 – 1) ÷ (.08 X 3.7000181)] X 1.08

[ 2.7000181 ÷ .2960014] X 1.08

9.1216383 X 1.08

9.8513693

So, after all that, we find out that our constant is 9.8513693. Now we simply divide our goal, which is $31,580 by our constant to get our payment amount.

$31,580 ÷ 9.8513693 = $3,205.65

So, we have found out that if we take the $3,000 we already have saved and add $3,205.65 to it at the beginning of each year at an 8% return, we will be able to fund Hector’s college. Keep in mind that this $3,205.65 must be saved through Hector’s college.

In Part IV of this series I’ll show an example of a timeline so you can see how all this works.

*This is the formula for payments made at the beginning of the time period, called an “annuity due.” The other formula is called an “ordinary annuity.” For more on this, you can visit this website.

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