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.
, 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](https://tex.z-dn.net/?f=r%3D3%5C%25%3D%5Cfrac%7B3%7D%7B100%7D%3D0.03)
1 month will be equal to
.
![\$10=P\cdot0.03\cdot \frac{1}{12}](https://tex.z-dn.net/?f=%5C%2410%3DP%5Ccdot0.03%5Ccdot%20%5Cfrac%7B1%7D%7B12%7D)
![\$10=0.0025P](https://tex.z-dn.net/?f=%5C%2410%3D0.0025P)
![\frac{\$10}{0.0025}=\frac{0.0025P}{0.0025}](https://tex.z-dn.net/?f=%5Cfrac%7B%5C%2410%7D%7B0.0025%7D%3D%5Cfrac%7B0.0025P%7D%7B0.0025%7D)
![P=\$4000](https://tex.z-dn.net/?f=P%3D%5C%244000)
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}](https://tex.z-dn.net/?f=I%3D%5C%242500%5Ccdot%200.03%5Ccdot%20%5Cfrac%7B1%7D%7B12%7D)
![I=\$6.25](https://tex.z-dn.net/?f=I%3D%5C%246.25)
Since the account earns an amount of $6.25 in one month, therefore, the poster is not true.