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.
[tex]I=Prt[/tex], where,
I = Amount of interest,
P = Principal amount,
r = Annual interest rate in decimal form,
t = Time in years.
[tex]r=3\%=\frac{3}{100}=0.03[/tex]
1 month will be equal to [tex]\frac{1}{12}[/tex].
[tex]\$10=P\cdot0.03\cdot \frac{1}{12}[/tex]
[tex]\$10=0.0025P[/tex]
[tex]\frac{\$10}{0.0025}=\frac{0.0025P}{0.0025}[/tex]
[tex]P=\$4000[/tex]
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.
[tex]I=\$2500\cdot 0.03\cdot \frac{1}{12}[/tex]
[tex]I=\$6.25[/tex]
Since the account earns an amount of $6.25 in one month, therefore, the poster is not true.
