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?
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.
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.
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.
What school gives this impossible question?
Besides -- the father isn't giving his son a gift if he takes away his allowance!
Yikes!
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
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!
To determine the type of investment that will guarantee you will have enough in the account to pay for the trip in June of your son's senior year, you need to consider a few factors:
1. Time horizon: You mentioned that you're starting in your son's second semester as a high school junior and that you want to save enough money by June of his senior year. This gives you approximately 1.5 years (18 months) to save.
2. Target amount: You mentioned that you want to save $4,000 for the trip expenses for your child and two of his closest friends.
3. Risk tolerance: Different investment options come with different levels of risk. Higher-risk investments can potentially offer higher returns, but they also come with a greater chance of losing money. Your risk tolerance will play a significant role in deciding the type of investment you should consider.
Having considered these factors, let's explore a few potential investment options:
1. High-yield savings account: A high-yield savings account is a low-risk option that offers slightly higher interest rates compared to traditional savings accounts. However, it's essential to note that interest rates are currently low. You could research different banks and compare their interest rates to find the best option. Keep in mind that this might not be enough to guarantee $4,000 in 1.5 years.
2. Certificate of Deposit (CD): CDs are time deposits with fixed interest rates. They generally offer higher interest rates than regular savings accounts but require you to lock your money for a specific period, such as 1 to 2 years. You could invest your $25 weekly allowance into a CD and choose a term that expires around June of your son's senior year. This may help guarantee that you'll have enough money for the trip.
3. Mutual funds or index funds: Mutual funds and index funds invest in a diversified portfolio of assets, such as stocks or bonds. They can potentially provide higher returns than savings accounts or CDs, but they also come with a higher level of risk. Over a 1.5-year period, investing in an equity-based index fund could offer growth potential, considering historical stock market trends. However, it's important to note that there are no guarantees with the stock market, and your investment could lose value. Be sure to consult with a financial advisor before considering this option.
Remember, investing involves risk, and no investment can guarantee a specific return. It's important to do thorough research, understand your risk tolerance, and consult with a financial advisor to make an informed decision based on your individual circumstances.