Question

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!"?

Answer 1

Assuming that the 4.8% interest rate is an annual interest rate, then, after one year, with a principal of $3,000 we would be able to win 4.8% of $3000:

`3000*(4.8)/(100)=144`

Divide 144 over 12 to find the monthly earnings:

`(144)/(12)=12`

Therefore, with a principal of $3,000 we would be earning $12 interest in 1 month.

For the earnings on the first month to be equal to $10, then you would have to win $120 annually, and $120 must be 4.8% of the principal. To find which quantity satisfies that 4.8% of it is equal to $120, divide 120 over 4.8%:

`\frac{120}{4.8\text{ \%}}=(120)/((4.8/100))=(100)/(4.8)*120=2500`

Therefore, the principal must be equal to $2500 for you to win $10 on the first month, and it would indeed be correct to say that if you open an account with $3000 you will earn at least $10 interest in 1 month.