4.07 Project Assignment: Work Independently
You and some friends have started your own company. After the first few months, the profits are rolling in. It is time to start thinking about putting your money to work for you. You decide that investing $5,000 into some Certificates of Deposit (CDs) would be a beneficial move.
With a CD, you lend your money to a third party, and after a set time, your money is paid back with interest. Before you start investing the company's money this way, you need to pitch it to your friends.
1. Research the highest interest rate (APY—annual percent yield) for 2year and 5year CDs. Document the company's name, interest rate, and minimum investment. The minimum investment must be less than or equal to $5,000.
2. Create the functions that represent the 2year and 5year CDs with your $5,000 investment. Use these functions to determine the amount you will be paid when the CD matures (the length of time for the specific CD). Show your work.
3. An investor comes to your office. He says that if you give him the $5,000 he will add on an additional $50 each year to what he owes you. Create the function for this investor's plan.
4. Create a table showing the value of the two CD's and the investor's plan for 5 years.
5. Explain to your friends how to prove that the investor's plan is a linear function and the CDs are exponential functions. Use complete sentences.
8. Make a final recommendation on what plan you and your friends should follow. Consider that you cannot collect your money from a CD until it has fully matured. Your recommendation should be at least three sentences long.
6. Find the average rate of change for the investor's plan and the 5year CD between years 2 and 3, and between years 3 and 5. Explain what this shows in complete sentences.
7. One of your friends suggests another 5year option that gives interest based on the function k(x) = 5000(1.02)^x. Explain what the 1.02 represents in terms of the CD and if it is a better plan than the 5year CD you found. Use complete sentences.
The highest interest rate (APY) for a 2 year CD is 0.5000% from Tropical Financial Credit Union and has a minimum investment of $500.
The highest interest rate (APY) for a 5 year CD is 1.2500% from Tropical Financial Credit Union and has a minimum investment of $500.
2 year CD

F(x) = 500(0.5000)x.

Total amount: 1750
5 year CD

F(x) = 500(1.2500)x.

Total amount: 1525.88
f(x) = 5,000 + 50x
The investor's plan is linear because the function increases at a steady rate (50). The CD's are exponential functions because the are both multiplied by a common ratio (0.5000 {2year CD} and 1.2500 {5year CD}.
The rate of change for the investor's plan is 50. The average rate of change for the 5year CD from year 23 is: $195.31. The average rate of change from year 35 is: $274.66
1.02 represents the average rate of change. The new 5year CD is way better than the 5year CD that I found because my CD ends up with $1525.88 and the new CD ends up with $5520.40.
I think that we should use the new CD because even though we cannot collect our money until the CD has completed, we will have more money as a whole. The 2year CD would give us money faster, but would not give us as much money. The 5year CD wouldn't give us as much money as even the 2year CD (what a ripoff)! But the new 5year CD will give us quite a bit more money (with quite a bit more patience).
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4.07 Algebra 1 Joshua Fernandez
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