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Meeting Future Goals

By JLP | February 6, 2006

I recieved the following email last night and thought I would answer her question in a post. Here’s the email:

I was wondering if you could help me with a problem that I have for my class. I was searching on Google and I found you page. I tried to follow it with the information I have from my problem, but I seem to be doing it wrong still. I have a present value annuity problem. This is the problem:

Child 1 will go to college in 11 years.

Child 2 will go to college in 13 years.

The annual interest rate will be 10 per cent and will be compounded annually.

I will need $25,000 per child per year of college for four years of college for each child.

How much must I put away each year beginning at the end of this year?

Compute the annual payment to be made each year so that I will have exactly covered the required amounts when the second child completes the fourth year of college. As a simplifying assumption, we will assume that the college will allow a single tuition payment to be made at the end of each year. I want to put away the same amount every year until the obligation is completed.

If you could just give me some direction as to what to do I would be very greatful. Thank you for your time.


My Response

The easiest way to calculate this is to set up an Excel Spreadsheet calculating the present value for each of the years using this formula:

Amount Needed ÷ (1 + ROR)N

ROR is Rate of Return which is 10% or .10. N is the number of years until the money is needed.

So, the present value of Child 1’s first year of college looks like this:

$25,000 ÷ (1 + .10)11

$25,000 ÷ 2.8531167

$8,762

I performed all the calculations in Excel and posted the results in the table below:


Child 1

Child 2

# of
Years Away

Amount
Needed

PV of
Amount
Needed

# of
Years Away

Amount
Needed

PV of
Amount
Needed

11

$25,000

$8,762

13

$25,000

$7,242

12

$25,000

$7,966

14

$25,000

$6,583

13

$25,000

$7,242

15

$25,000

$5,985

14

$25,000

$6,583

16

$25,000

$5,441

Total PV for Child 1

$30,553

Total PV for Child 2

$25,251

If we sum the present value totals for both children, we know that we need to invest $55,803.43 today at a 10% ROR in order to meet the future college expenses. However, her question was how much would she have to invest at the end of each year in order to fully fund the college expenses for both children. In order to figure this out, we must use the formula for an annuity. Since she wants to invest at the END of each year, we will use the formula for an ordinary annuity to solve for the annuity factor, which looks like this (it looks kind of hairy):

[(1 + ROR)N – 1] ÷ [ROR X (1 + ROR)N]

ROR is rate of return, N is the number of years and the X is the multiplication sign. So, plugging in the numbers, the formula now looks like this:

[(1 + .10)16 – 1] ÷ [ .10 X (1 + .10)16]

[ 1.1016 – 1] ÷ [ .10 X (1.1016)]

[ 4.5949730 – 1] ÷ [ .10 X 4.5949730]

3.5949730 ÷ .45949730

7.8237087

This is our annuity factor. To find out how much must be saved at the end of each year, you simply divide $55,803.43 by the factor (7.8237087), which gives us $7,132.61. So, if she would begin saving $7,132.61 at the end of this year and it grew at an 10% per year, she would have enough to pay for both educations.

Wow! That was a long post!

Topics: College Funding | 4 Comments »


4 Responses to “Meeting Future Goals”

  1. Kurt Says:
    February 6th, 2006 at 6:07 pm

    Doesn’t that assume no taxes? Presumably she won’t be able to realize 10% on an after-tax basis.

  2. Bored Says:
    February 6th, 2006 at 8:52 pm

    Man, you just did someone’s homework for them! (I wish the internet was around when I was in school.

    Now, lets say two cars are moving in opposite directions, one at 45 KPH and the other at 60 KPH.

    How long will it take…

    But seriously, nice work! In July, my second child will be born, and the thought of funding 2 seperate educations is quite daunting…luckily I have 16 and 18 years, respectively, to do it! :D

    Luckily, Kurt, there are many options to avoid taxes on education-oriented investments (ie. 529 plans)

  3. MoneyDummy Says:
    February 6th, 2006 at 9:06 pm

    I’m beginning to think that my parents had a wise approach:
    “Children, if you want to go to college, do extremely well in
    school because scholarships are the only way you’ll be able to
    afford it.”

    It’s worked for the three oldest girls thus far. LOL.

  4. Brian Says:
    February 7th, 2006 at 11:32 am

    Inflation cost for college cost is also not considered. BTW college cost inflation has been greater than CPI over the last few years. BTW2 where can I find that 10% return for the next 16 years? ;)

Comments