I can help you with that! To calculate the capital that, at an annual interest rate of 6% for 20 days, has produced an interest of $30, you can use the following formula:
\[ \text{Interest} = \frac{\text{Capital} \times \text{Rate} \times \text{Time}}{365} \]
Given:
- Interest = $30
- Rate = 6%
- Time = 20 days
First, convert the rate to a decimal by dividing it by 100:
\[ \text{Rate} = \frac{6}{100} = 0.06 \]
Now, calculate the capital:
\[ 30 = \frac{\text{Capital} \times 0.06 \times 20}{365} \]
\[ 30 = \frac{0.12 \times \text{Capital}}{365} \]
\[ \text{Capital} = \frac{30 \times 365}{0.12 \times 20} \]
\[ \text{Capital} = \frac{10950}{2.4} \]
\[ \text{Capital} = 4562.5 \text{ dollars} \]
Therefore, the initial capital that, at a 6% annual interest rate for 20 days, has produced $30 in interest is $4562.50.
