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:
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:
I performed all the calculations in Excel and posted the results in the table below:
Child 1 |
Child 2 |
||||
# of |
Amount |
PV of |
# of |
Amount |
PV of |
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):
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:
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!
Doesn’t that assume no taxes? Presumably she won’t be able to realize 10% on an after-tax basis.
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! ðŸ˜€
Luckily, Kurt, there are many options to avoid taxes on education-oriented investments (ie. 529 plans)
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.
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? ðŸ˜‰