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04.07 Exploring Linear and Exponential Growth

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adrian chamberlin

on 8 May 2014

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Transcript of 04.07 Exploring Linear and Exponential Growth

04.07 Exploring Linear and Exponential Growth
It's been four months since Cash Cow Credit Union has opened and since then it has been quite a lucrative business. But i believe it is time to invest in some CD's.

I have made table of possible investments.
04.07 Exploring Linear and Exponential Growth
My friends and I have started our own company (NumberZ&Stuff). After the first few months, the profits come rolling in and it’s time to start thinking about putting our money to work for us. We’ ve 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, the money is paid back with interest. But a few of my friends are still skeptical about it, so before we start investing the company's money this way, I need to pitch it to my friends.
One of my friends suggests another 5-year option that gives interest based on the function k(x) = 5000(1.02) x. He asked me to explain what 1.02 represents in terms of the CD and if it is a better plan than the 5-year CD I had found. The average rate of change for k(x) = 5000(1.02)^x would be1.02. The old 5-year CD would develop into $1525.88, but with the new 5-year CD would end up developing in $5520.40. Making the new CD better than the one I found.
Later an investor comes to our office. He says that if we gave him the $5,000 he will add on an additional $50 each year to what he owes us. Here is a function for this investor's plan.

[F(x) = 5,000 + 50x]

I have took it upon myself to research the highest interest rate (APY—annual percent yield) for the 2-year and 5-year CDs. The highest interest rate (APY) for the 2-year CD would be 0.7000 %(At Cash Cow Credit Union) with a minimum investment of $700.And the highest interest rate (APY) for the 5-year CD is 1.2500 %(At Cash Cow Credit Union) with a minimum investment of $700.
I also found that the average rate of change for the investor's plan is $50 and the 5-year CD between years 2 and 3 would be: $195.31, and between years 3 and 5 is: $274.66.
I have also created functions that represent the 2-year and 5-year CDs with your $5,000 investment. And also used these functions to determine the amount we will be paid when the CD matures (the length of time for the specific CD).
2-year CD|F(x) = 700(0.5000)x.|Full amount: 1750
5-year CD|F(x) = 700(1.2500)x.|Full amount: 1525.88

Year 1 Year 2 Year 3 Year 4 Year 5
2-year CD 750 1250 1750 2250 2750
5-year CD 625 781.25 976.56 1220.70 1525.88
Investor’s 5,050 5,100 5,150 5,200 5,250

Here is a table of the increase of revenue.
Overall I believe we would be better off with the new 5-year CD. I think this is the best chose because the investment will turn into a larger sum then the others. We won’t be able to have the money until the 5 years are up, but seem the most profitable of all the choices. The 2-year CD would be faster, but is not as profitable as the new 5-year plan. The old 5-year would beneficial as the new 5-year CD or even the 2-year CD.
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