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

The principle should be $4000 to earn $10 in one month with the simple interest rate of 3 percent thus the poster is incorrect which says open an account of $3500 and earn at least $10 interest in 1 month.

Given-

The simple interest rate is 10 percent.

The simple interest for the one month is 10.

Let the principle be [tex]p[/tex] to earn $ 10 in one month with the simple interest rate of 3 percent.

The formula for the simple interest [tex]S_i[/tex] of one month for principle [tex]p[/tex], simple interest rate [tex]r[/tex] time [tex]t[/tex] can be given as,

[tex]S_i=\dfrac{p\times r\times \dfrac{t}{12} }{100}[/tex]

[tex]S_i=\dfrac{p\times r\times t}{100\times12}[/tex]

Put the value of known values,

[tex]10=\dfrac{p\times 3\times 1 }{100\times 12}[/tex]

Rewrite the equation for [tex]p[/tex],

[tex]p=\dfrac{100\times 12 }{3}[/tex]

[tex]p=4000[/tex]

Hence, the principle should be $4000 to earn $10 in one month with the simple interest rate of 3 percent.

Now according to the poster which says open an account of $3500 and earn at least $10 interest in 1 month-This statement is not correct as to earn $10 in 1 month one should open an account of $4000.

Hence, the principle should be $4000 to earn $10 in one month with the simple interest rate of 3 percent thus the poster is incorrect which says open an account of $3500 and earn at least $10 interest in 1 month.

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