To calculate the interest accrued at the end of the second month on the amounts you invested, you can use the formula for simple interest:
\[ \text{Interest} = P \times r \times t \]
Where:
- \( P \) = principal amount (the amount of money invested)
- \( r \) = annual interest rate (as a decimal)
- \( t \) = time in years
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First Month Investment:
- \( P_1 = 75.00 \)
- \( r = 3.75% = 0.0375 \)
- For the first month, \( t_1 = \frac{1}{12} \) years
\[ \text{Interest for first month} = 75.00 \times 0.0375 \times \frac{1}{12} \]
\[ \text{Interest for first month} = 75.00 \times 0.0375 \times 0.0833 = 0.234375 \]
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Second Month Investment (including the first month's interest):
- First, calculate the interest on the first month's investment for the second month:
\[ \text{Interest for second month on first investment} = 75.00 \times 0.0375 \times \frac{1}{12} \quad (\text{same as above}) \]
\[ \text{Interest for second month on first investment} = 0.234375 \]
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Now calculate the interest on the second month investment:
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\( P_2 = 1000.00 \)
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For the second month, \( t_2 = \frac{1}{12} \) years
\[ \text{Interest for second month on second investment} = 1000.00 \times 0.0375 \times \frac{1}{12} \]
\[ \text{Interest for second month on second investment} = 1000.00 \times 0.0375 \times 0.0833 = 3.125 \]
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Total Interest at the end of the second month:
\[ \text{Total interest} = \text{Interest from first month} + \text{Interest from second month on first} + \text{Interest from second month on second} \]
\[ \text{Total interest} = 0.234375 + 0.234375 + 3.125 \approx 3.59375 \]
Thus, rounding this calculation to two decimal points gives approximately $3.59.
The correct response from the options given is $3.59.
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