# Math Help - College Savings Plan

1. ## College Savings Plan

Hey Guys,

I am trying to figure out this problem dealing with a college savings plan for my kids.
Its currently September.....my kids are 14,13, and twins at 11. They are all planning on going to college in September of the year they turn 18. We estimate that tuition will cost 5642 per year for each of their four years of college assuming 0% inflation. We want to calculate our savings plan with a 3% annual interest rate compounded monthly.

How much should I save each month in my savings plan?

Thanks.

2. ## Re: College Savings Plan

If you put S dollars in the bank each month then in n months it will have increased to $S(1+ .03/12)^n= S(1.0025)^n$. Of course, each month you will have one less month for the money added that year to accrue interest. That is the money put in the bank the first year will earn $S(1+ .03/12)^n$, the money put in the second month will have earned $S(1.0025)^{n-1}$. That means that if you have a total of n months to save, and put S dollars in the account each month, at the end of those n months you will have $S+ S(1.0025)+ S(1.0025)^2+ \cdot\cdot\cdot+ S(1.0025)^{n-1}+ S(1.0025)^n$. That is a "geometric" series, of the form $\sum Ar^i$ with A= S and r= 1.0025. It is easy to show that the sum of such a geometric series is $A\frac{1- r^{n+1}}{1- r}$. For your sum that is $S\frac{1.0025^{n+1}- 1}{.0025}$. Put in the number of months you will have to save for each one, set it equal to 5642, and solve for S. For given n, $\frac{1.0025^n- 1}{.0025}$ is a specific number and solving for S means just dividing 5642 by that number.

3. ## Re: College Savings Plan

Thanks for the help !