To find the principal that would earn $10 in interest in one month at a simple interest rate of 3%, we can use the formula for simple interest:
\[ I = P \cdot r \cdot t \]
Where:
- \(I\) is the interest earned,
- \(P\) is the principal,
- \(r\) is the interest rate (as a decimal),
- \(t\) is the time (in years).
Since we want to find the principal for one month, we convert one month into years by dividing by 12:
\[ t = \frac{1}{12} \text{ years} \]
Given:
- \(I = 10\) dollars,
- \(r = 3% = 0.03\).
Plugging these values into the formula, we get:
\[ 10 = P \cdot 0.03 \cdot \frac{1}{12} \]
To find \(P\), we rearrange the equation:
\[ P = \frac{10}{0.03 \cdot \frac{1}{12}} \]
Calculating the denominator:
\[ 0.03 \cdot \frac{1}{12} = \frac{0.03}{12} = 0.0025 \]
Now we substitute it back:
\[ P = \frac{10}{0.0025} = 4000 \]
So, the principal needs to be $4,000 to earn $10 in interest in the first month.
To answer the final question, regarding whether the bank manager can correctly say, "Open an account of $3,000 and earn at least $10 interest in 1 month!" based on this calculation:
Since $4,000 is higher than $3,000, the statement on the poster would not be accurate.
Therefore, to summarize:
- The principal needs to be $4,000.
- The poster should not say that one can earn at least $10 in interest with a principal of $3,000.
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