Question

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.BankPrincipalBalanceSuper Save$10006 $1173.34Star Financial $2500 3 $2684.35Better Bank$40005 $4525.63YearsThe investor chooses Better Bank because it earned over $100per year, which is much more than the other banks earned per year.Create a presentation to the investor explaining which bank is the best choice, basedon the given information. Include for each bank1. a graph showing how the investment would grow over a 10-year period, and2. the interest rate, including how you found it.

Answer 1

Step 1: Write the formula to be used

For a sum compounded annually

`A=P(1+r)^n_{^{^{}}}`

Step 2: Find the rates for each bank

Super save

`\begin{gathered} 1173.34=1000(1+r)^6 \\ (1+r)^6=(1173.34)/(1000)=1.117334 \\ (1+r)^6=1.117334 \\ 1+r=\sqrt[6]{1.117334} \\ 1+r=1.01866 \\ r=1.01866-1 \\ r=0.01866 \\ r=1.867\text{ \%} \end{gathered}`

For star Financial

`\begin{gathered} 2684.35=2500(1+r)^3 \\ (1+r)^3=(2684.35)/(3500)=1.07374 \\ (1+r)=\sqrt[3]{1.07374} \\ 1+r=1.02400 \\ r=1.02400-1=0.02400 \\ r=2.4\text{ \%} \end{gathered}`

For Better Bank

`\begin{gathered} 4525.63=4000(1+r)^5 \\ (1+r)^5=(4525.63)/(4000) \\ (1+r)^5=1.1314 \\ 1+r=\sqrt[5]{1.1314} \\ 1+r=1.025 \\ r=1.025-1 \\ r=0.025 \\ r=2.5\text{ \%} \end{gathered}`

Based on the interest rates, Better Bank has the highest interest rate

For the Better Bank,

The rates,

r= 2.5%

P=$5000

where n is less than or equal to 10 years

We will use the equation

`A=P(1+r)^n_{}`

To plot the graph

`A=5000(1.025)^n_{}`