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Bank On ItAn investor has $5000 to invest for 10 years in one of thebanks listed below. Each bank offers an interest rate that iscompounded annually.BankPrincipal Years BalanceSuper Save $10006 $1173.34Star Financial $2500 3 $2684.35Better Bank $4000 5 $4525.63The investor chooses Better Bank because it earned over $100per year, which is much more than the other banks earned per year.1. a graph showing how the investment would grow over a 10-year period, and2. the interest rate, including how you found it.Be creative in your presentation. Remember, you want to convince an investor whichbank is the best choice! I only need help with the graph part

Bank On ItAn Investor Has 5000 To Invest For 10 Years In One Of Thebanks Listed Below Each Bank Offers An Interest Rate That Iscompounded AnnuallyBankPrincipal class=

Sagot :

EXPLANATION

First, we need to apply the compounding interest equation as given below:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Where A=balance, P=principal, r=interest rate, n=number of times interest rate is compounded (in this case the interest rate is compounded annually, so n=1)

First, we need to isolate the interest rate from each bank.

Isolating r from the Compounding interst equation:

(Dividing both sides by P):

[tex]\frac{A}{P}=(1+\frac{r}{n})^{nt}[/tex]

Applying the nt root to both sides:

[tex]\sqrt[nt]{\frac{A}{P}}=(1+\frac{r}{n})[/tex]

Removing the parentheses:

[tex]\sqrt[nt]{\frac{A}{P}}=1+\frac{r}{n}[/tex]

Subtracting -1 to both sides:

[tex]\sqrt[nt]{\frac{A}{P}}-1=\frac{r}{n}[/tex]

Multiplying both sides by n. As n=1 we can desestimate this step.Additionally, as n=1 --> nt=1*t = t

[tex]\sqrt[t]{\frac{A}{P}}-1=r[/tex]

Switching sides:

[tex]r=\sqrt[t]{\frac{A}{P}}-1[/tex]

Now we can compute the interest rate for each bank as follows:

[tex]r_{Super\text{ Save}}=\sqrt[6]{\frac{1173.34}{1000}}-1[/tex][tex]r_{\text{Super Save}}=\sqrt[6]{1.17334}-1[/tex][tex]r_{\text{Super Save}}=1.027000479-1=0.0700047876[/tex]

As r is represented in decimal form, the r_Super Save= 2.70%

Applying the same reasoning to Star Financial:

[tex]r_{\text{Star Financial}}=\sqrt[3]{\frac{2684.35}{2500}}-1[/tex][tex]r_{\text{Star Financial}}=\sqrt[3]{1.07374}-1[/tex][tex]r_{\text{Star Financial}}=1.02399942-1=0.02399942017[/tex]

As r is represented in decimal form, the r_Star Financial= 2.39%

Applying the same reasoning to Better Bank:

[tex]r_{\text{Better Bank}}=\sqrt[5]{\frac{4525.63}{4000}}-1[/tex][tex]r_{\text{Better Bank}}=\sqrt[5]{1.1314075}-1[/tex][tex]r_{\text{Better }}=1.024999871-1[/tex][tex]r_{\text{Better Bank}}=0.02499987[/tex]

As r is represented in decimal form, the r_Better Bank= 2.49%

Now, that we have the interest rate values, we can build a table for each year corresponding to each Bank:

In order to draw the graph and using the table, we need to compute the balance for each year applying the above equation:

[tex]\text{B}=P(1+\frac{r}{n})^{nt}[/tex]

Note: (Commas and periods are reversed, Spreadsheet Configuration issue)

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