You are faced with a future obligation... Thirteen years from now your child wil

Question

You are faced with a future obligation... Thirteen years from now your child will enter college and you have promised to pay for their tuition. If you happen to know that in thirteen years from now, tuition will be $25,000 per year (payable at the beginning of the school year), how much money put away would cover this obligation if you assume your child will take four years to graduate and the interest rate is:

(a) 5%?

(b) 10%?

(c) 15%?

(d) 20%?

I really only need to see the process for one, maybe two of the above interest rates to get the idea.

Here's what I tried for (a) which is similar to what I did for all four parts:

Thanks!

Explanation / Answer

For starters, your PV formula is correct. However, the problem with what you have for (a) is that you assume a future value of $100,000 when in fact we are dealing with an annuity problem.

If I wanted 25,000 in thirteen years I would need to put away 13,258. I got this number from finding the present value of 25,000 at 5% interest with 13 periods.

If I wanted 25,000 in fourteen years (her second year at college), I would need 12,626.70. I got this from finding the present value of 25000 at 5% interest withg 14 periods.

If I want 25000 in 15 years I do the same calculation but with 15 periods and I get 12,025.43

For the last payment, which will take place 16 years from now, I need 11,452.79.

Adding these all up I get 13,258 + 12,626.7 + 12,025.43 + 11,452.79 = $49,362.92

Ass you can see, my answer is slighlty lower than yours because I am continuing to accrue interest on the remaining funds while she is still in college. Therefore I need to put away a smaller amount of money because I will gain three years of additional interest on this money.

Now, I don't know how your professor wants you to do it, but I think you might want to just do it like I did but change the interest rates for parts b, c, and d. Just calculate the present value of 25,000 using a calculator (like I did) or if you want to use that forumula simply do it four times for each part but do it like this:

25,000/(1+1.X)^n

Where X is the interest rate that should be changed for each part, and n us the number of years that should be changed with each calculation. You will do four calculations per part, increasing n by 1 every time. Hope this helps. Don't forget to rate.

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