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

Answer:

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  

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

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

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

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 = $= \frac{1}{12} year$

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

So, the statement is correct.

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