**Assignment 4.07**

**By: Jordyn Gartner**

1. Research the highest interest rate (APY—annual percent yield) for 2-year and 5-year CDs. Document the company's name, interest rate, and minimum investment. The minimum investment must be less than or equal to $5,000.

The company name i got was CIT bank, the highest interest rate for the 2 year CD was 1.25% and a minimum investment of $1000 for the 5 year CD it was 2.30% and a minimum investment of $1000.

2.Create the functions that represent the 2-year and 5-year 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

For the function for the 2 year i put : f(x)=5000(1.0125)^x and i got $5125.80 and for the 5 year function i put f(x)=5000(1.0230)^x and i got $5602.10. I got this by plugging in 2 for the years for the first equation and 5 for the years in the second since it was the amount of years for the plan.

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.

The function would be: f(x)=5,000+50x

Year 1 Year 2 Year 3 Year 4 Year 5

2-year CD 5062.50 5125.8 x x x

5-year CD 5115.00 5232.60 5353 5476.10 5602.10

Investor 5,050 5,100 5,150 5,200 5,250

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.

The investors plan is a linear function because it increases at a steady rate. CDs grow at a continuous ratio over the years which changes the starting amount yearly.

6.Find the average rate of change for the investor's plan and the 5-year CD between years 2 and 3, and between years 3 and 5. Explain what this shows in complete sentences.

The investors plan is linear and the rate of change for it is 50 per year. The rate of change is 120.40 for year 2 to 3 and 249.10 for years 3- 5. The CDs both exponential functions because they're multiplied by common ratios and numbers.

7.One of your friends suggests another 5-year 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 5-year CD you found. Use complete sentences.

1.02 represents the average rate of change.Where.02 represents the interest rate which was 2% and mine is better because my interest rate was 2.3%.

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.

The plan i recommend is my 5 year cd. I chose this because with the 2 year cd, although it will be less amount of time it wont end up as much. My 5 year Cd will take longer but it will be worth it because it will finish with more money over time. The new Cd will come out as less then my 5 year CD, too. So in my opinion i think my friends and i should use my 5 year CD, because we'll end up with more money.