Question

A bank manager wants to encourage new customers to open accounts with principals of at least ​$2 comma 500. He decides to make a poster advertising a simple interest rate of 3​%. 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 ​$2 comma 500 and earn at least ​$10 interest in 1​ month!"?

Answer 1

Answer:

To earn $10 in 1st month, the principal must be $4,000.

No, the poster cannot claim that "Open an account of ​$2 comma 500 and earn at least ​$10 interest in 1​ month!".

Step-by-step explanation:

We have been given that a bank manager wants to encourage new customers to open accounts with principals of at least ​$2,500. He decides to make a poster advertising a simple interest rate of 3​%. We are asked to find the principal to advertise that one can earn ​$10 the first​ month.

We will use simple interest formula to solve our given problem.

$I=Prt$, where,

I = Amount of interest,

P = Principal amount,

r = Annual interest rate in decimal form,

t = Time in years.

$r=3\%=\frac{3}{100}=0.03$

1 month will be equal to $\frac{1}{12}$.

$\ 10=P\cdot0.03\cdot \frac{1}{12}$

$\ 10=0.0025P$

$\frac{\ 10}{0.0025}=\frac{0.0025P}{0.0025}$

$P=\ 4000$

Therefore, to earn $10 in 1st month, the principal must be $4,000.

Now, we will check if an account of ​$2,500 can earn at least ​$10 interest in 1​ month.

$I=\ 2500\cdot 0.03\cdot \frac{1}{12}$

$I=\ 6.25$

Since the account earns an amount of $6.25 in one month, therefore, the poster is not true.