Question

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​%. 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 ​$3,500 and earn at least ​$10 interest in 1​ month!"?

Answer 1

The poster say, "Open an account of ​$3,500 and earn at least ​$10 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 } * \text {rate} * \text {time}}{100}`

In our problem, simple interest = $10, rate = 4.8%, time = 1 month
`= (1)/(12) year`

`\begin{array}{l}{\text { Then, } 10=\frac{\text { amount } * 4.8 * (1)/(12)}{100}} \\\\ {\text { Amount } * 4.8 * (1)/(12)=1000} \\\\ {\text { Amount } * 0.4=1000} \\\\ {\text { Amount }=(1000)/(0.4)=\$ 2500}\end{array}`

Let us see Can the poster correctly say, "Open an account of $3,500 and earn at least $10 interest in 1 month!"?

So now, in our problem, amount = $3500, rate = 4.8% and time = 1 month =
`= (1)/(12) year`

`\text { Then, simple interest }=(3500 * 4.8 * (1)/(12))/(100)=35 * 4.8 * (1)/(12)=35 * 0.4=14`

So, the statement is correct.

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