Posted by David on .
As a graduation present, you want to gift your son a trip to Disney World. Presently beginning his second semester as a high school junior, you hope you have enough time to save $4,000 to support much of the trips expenses for your child and two of his closest friends. Rather then giving him his normal $25 a week allowance, you decide to start investing that money for the trip. What type of investment will Guarentee you will have enough in the account to pay for the trip in June of his senior year?

Algebra 2 
Ms. Sue,
No investment will guarantee you that kind of interest or dividends.
The only guaranteed investments for this period of time are certificates of deposit, savings accounts, and money market accounts. At best, they are paying about 1% apr. 
Algebra 2 
Ms. Sue,
If you invest $25 a week for 1 1/2 years, the best you can hope for is about $2,000, about half of your goal.

Algebra 2 
Reiny,
So I will assume you are working at 52 weeks a year, with a time of 2 years, making it 104 deposits of $25
( I am not familiar with the terminology of naming the years in college, I will assume that a "junior" is in the 3rd year ? )
let the weekly rate be i
25((1+i)^104  1)/i = 4000
This is not an easy equation to solve, and would require something along the lines of Newton's Method to solve. I will "cheat" and use Wolfram to solve it
http://www.wolframalpha.com/input/?i=25%28+%281%2Bx%29%5E104++1%29%2Fx+%3D+4000
it gave me i = .0078618 (I used x in the equation)
so the annual rate compounded weekly is
.4088 or 40.88%
As Ms Sue pointed out, this is a totally ridiculous rate of interest, making this a rather silly question. 
Algebra 2  P.S. 
Ms. Sue,
What school gives this impossible question?
Besides  the father isn't giving his son a gift if he takes away his allowance!
Yikes! 
Algebra 2 
David,
Thanks Ms Sue its my daughters problem ,my responce was maybe the wording might be asking "what investment " might be what amounts in what types of investments would yield the $4ooo. Or it might be just be about the math and analizing it. Either way ,thank you

Algebra 2 
Ms. Sue,
You're welcome.
I'd certainly look into the kind of education your daughter is getting. This question misuses the word "gift," as well as posing a ridiculous math problem. It gives students the idea that they can "invest" and make tons of money. That simply is not true!