Question

Where am I going wrong? Please help

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.

Answer 1

This is what I have so far from my researched company.
Discover Bank: 1.15%, $2,500 2-year CD
Discover Bank: 2.10%, $2,500 5-year CD

Answer 2

To follow up, it says to create a function that represents this scenario for the 2-Year CD & 5-Year Cd and show how much you will be paid when the CD matures.

This is my work thus far, but it seems fishy, it looks too good to be true?

F(x) = 2500(1.15)^2 = 2500(1.32) = $3,300
F(x) = 2500(2.10)^5 = 2500(40.84) = $102,100

Answer 3

I wish I could help you out, but I don't know anything about economics type stuff. Good luck, hopefully someone shows up soon, if not maybe try checking back tomorrow and bumping it?

Answer 4

your equations are right
use 5000 rather than 2500.

https://prezi.com/xjfsynwyj39m/407-407-exploring-linear-and-exponential-growth/

exact same problem here expand the comments

Answer 5

What formula are you using, can you write it out without the values but with variables in their stead?

Answer 6

F(x) = a * (r) ^ x it could be that, if that makes more sense @Algorithmic

Answer 7

Does that work for annual percent yield? If I recall correctly:
\[APY = (1 + \dfrac{r}{n})^n - 1\]
Let \(r\) be rate.
Let \(n\) be compound periods per year.

So now plug it all in:
\[APY = (1 + \dfrac{0.0115}{2})^2 - 1\]
\[0.0115330625 = 1.1533062\%\]
\($2,500 * 0.0115330625 = $28.83\) earning?

That seems awfully small...

Answer 8

Exactly this is where I'm stuck, however that formula seems to make sense, It makes more sense then making over $100,000 from only 2,500 in 5 years however

Answer 9

That would mean that for the 5 Year CD it would be
APY = (1 + 0.0210 / 5) ^ 5 - 1

correct?

Answer 10

Let me calculate for the second one, however I am still skeptical we are using the correct formula.

\[APY = (1 + \dfrac{r}{n})^n - 1\]
\[APY = (1 + \dfrac{0.021}{5})^5 - 1\]
\[APY = 0.02117714243715491232\]
\[0.02117714243715491232 = 2.11771424371549123\%\]
\[2,500 * 0.02117714243715491232 = 52.9428560928872808~earning?\]

Five years should yield one more money, I think I am calculating something wrong. Let me try Google for some help, LOL.

Answer 11

Honestly its such a mind freak, LOL.

Answer 12

Indeed. Do you know under what chapter you are learning this? Maybe that could hint us in what we need to do?

Answer 13

Its called 04.07 Exploring Linear and Exponential Growth in Algebra I

Answer 14

Hmm, so it defiantly will not need my original thought of a economics formula, rather something with exponential growth/decay.

Answer 15

Well the formula you gave me was mentioned in the lesson, However I'm not sure if it would. apply to this scenario. the $52 increase for 5 years may be correct because of this scenario as well,
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.
F(x) = 5000 + 50x

Answer 16

Working this out on paper, I work better that way. Just a second.

Answer 17

That is fine, I am very thankful for your help!

Answer 18

This seems more right, so I hope it is.

Actual formula for exponential growth:
\[y = a_i(1 + r)^n\]
\(a_i = Initial~amount.\)
\(r = Rate.\)
\(n = Number~of~years~aka~time~of~growth.\)

Let:
\(a_i = 2,500\)
\(r = 1.15\% \rightarrow 0.0115\)
\(n = 2\)

So:
\[y = 2,500(1 + 0.0115)^2 = 2557.83\]

I tried for the second equation, and it works too. Try it, and I will confirm on your answer.

Answer 19

Alright so,

A= 2,500
R= 1.21% > 0.021
N = 5

y = 2500 (1 + 0.021) ^ 5 = $2773.7589 = $2774 ??

Answer 20

Close but: 1.21% = 0.0121.

Answer 21

Y = 2500 (1 + 0.0121) ^ 5

= 2654.9548 = $2655?

Answer 22

Correct!

\[y = 2500(1 + 0.0121)^5\]
\[y = 2500(1 + 0.0121)^5\]
\[(1 + 0.0121)^5 = 1.06198192304881474601\]
\[y = 2500 * 1.06198192304881474601\]
\[y = 2654.954807622036865025\]

Answer 23

THANK YOU SO MUCH!!! That makes much more logical sense & I completely see where I went wrong & will forever learn from this mistake! @Algorithmic you are the best! Have i already awarded you your much earned medal?

Answer 24

No problem, just glad I was of help. It was a nice refresher on exponential growth and decay for me. :-)

Peace.