A bank manager wants to encourage new customers to open accounts with principals of at least $3 comma 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 comma 000 and earn at least $10 interest in 1 month!"? The principal needs to be to earn 10 in interest the first month.

Question

A bank manager wants to encourage new customers to open accounts with principals of at least ​$3 comma 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 comma 000 and earn at least ​$10 interest in 1​ month!"? The principal needs to be ​ to earn ​10 in interest the first month.

GPT 3.5 · Answer

To calculate the principal needed to earn $10 in interest at a simple interest rate of 4.8% in one month, we can use the formula for simple interest:

Interest = Principal x Rate x Time

Given that the interest is $10, the rate is 4.8% (or 0.048), and the time is 1 month, we can plug in these values:

$10 = Principal x 0.048 x 1

Solving for Principal:

Principal = $10 / (0.048 * 1)
Principal = $10 / 0.048
Principal = $208.33

So, the principal needed to earn $10 in interest at a simple interest rate of 4.8% in one month is $208.33. Therefore, the poster cannot correctly say, "Open an account of $3,000 and earn at least $10 interest in 1 month" as the principal required to earn $10 in one month is $208.33.