Advertising A bank manager wants to encourage new customers to open accounts with principals of at least $3,000. He decides to make a poster advertising a simple interest rate of 4.8%. What must the principal be if the bank manager also wants to advertise that one can earn $10 the first month? Can the poster correctly say, "Open an account of $3,000 and earn at least $10 interest in 1 month!"?​

The poster say, "Open an account of 3,500 and earn at least 3,500andearnatleast10 interest in 1 month!" is correct

Solution:

Given, A bank manager wants to encourage new customers to open accounts with principals of at least $3,500.

He decides to make a poster advertising a simple interest rate of 4.8%.

We have to find what must the principal be if the bank manager also wants to advertise that one can earn $10 the first month

We know that, banks offer simple interest

\text { Simple interest }=\frac{\text { amount } \times \text {rate} \times \text {time}}{100} Simple interest =

100

amount ×rate×time

In our problem, simple interest = $10, rate = 4.8%, time = 1 month = \frac{1}{12} year=

12

1

year

\begin{gathered}\begin{array}{l}{\text { Then, } 10=\frac{\text { amount } \times 4.8 \times \frac{1}{12}}{100}} {\text { Amount } \times 4.8 \times \frac{1}{12}=1000} {\text { Amount } \times 0.4=1000} {\text { Amount }=\frac{1000}{0.4}=\$ 2500}\end{array}\end{gathered}

Then, 10=

100

amount ×4.8×

12

1

Amount ×4.8×

12

1

=1000

Amount ×0.4=1000

Amount =

0.4

1000

=$2500

Let us see Can the poster correctly say, "Open an account of 3,500 and earn at least3,500andearnatleast10 interest in 1 month!"?

So now, in our problem, amount = $3500, rate = 4.8% and time = 1 month = = \frac{1}{12} year=

12

1

year

\text { Then, simple interest }=\frac{3500 \times 4.8 \times \frac{1}{12}}{100}=35 \times 4.8 \times \frac{1}{12}=35 \times 0.4=14 Then, simple interest =

100

3500×4.8×

12

1

=35×4.8×

12

1

=35×0.4=14

So, the statement is correct.

Hence, amount to be invested is $2500 and poster says correctly.

i found two solutions,   n = 2 • ± √3 = ± 3.4641

step-by-step explanation: