College Funding Math - Part II

With the last post, we figured out that four years of college was expected to cost $105,655. Now we need to know how to reach that goal.

So that we don't have to keep referring back to the first post, here are the assumptions:

Assumptions: Hector (I figured we might as well have some fun with the name) is 5 years old and will start college when he is 18, which is 13 years away. You currently have $3,000 in Hector's college fund. One year at a public university currently costs $13,000 and we will assume that the college inflation rate is 5.0% (or .o5) per year. We will also assume that Hector will be in college for 4 years. We will assume the growth rate on the investment account is 8% (or .o8). Finally, we will assume that the annual amount saved will cease once Hector starts college.

Step 2 - Calculate the present value of four years of college

The costs for each of the four years of college are expected to be:

Year 1 = $24,513
Year 2 = $25,739
Year 3 = $27,026
Year 4 = $28,377
TOTAL = $105,655

In order to know how much we need now to meet these future expenses, we must discount them using our expected investment return, which is 8%. The formula for Present Value of a Lump Sum is:

Present Value = Future Value / (1 + ROR)^N
Future Value = $24,513
ROR = 8.0% or .08
N = 13 years
/ = the division sign

All plugged in, the formula looks like this:

Present Value = $24,513 / (1 + .08)¹³

Present Value = $24,513 / 2.7196237

Present Value = $9,014

What this tells us is that if we had $9,014 that we invested at an 8% return per year, we would have $24,513 in 13 years. We simply need to perform this calculation for each of the other three years of tuition and then add them together to get the total lump sum that we need NOW in order to fund Hector's college expenses.

Performing the calculation on the other three years of tuition, we get the following:

Year 1 = $ 9,014
Year 2 = $ 8,763
Year 3 = $ 8,520
Year 4 = $ 8,283
TOTAL = $ 34,580

So, this tells us that if we had $31,580 LUMP SUM (remember we ALREADY HAVE $3,000 SAVED UP, so the we only need $31,580 additional funds) to invest today at an 8% annual return, we would have enough to fully fund Hector's college education. The problem is that there aren't a whole lot of people who have an extra $33,159 sitting around to invest for college. Most people have to save smaller amounts each year. I'll talk about that in Part III.

Tags: Saving for College, College Funding, Time Value of Money