interest in 3 months is 66420 now find the rate of interest and principal

To find the rate of interest and the principal, we need to use the formula for simple interest:

\[
\text{Simple Interest (SI)} = \frac{P \times R \times T}{100}
\]

Where:
- \( SI \) is the Simple Interest (given as 66,420).
- \( P \) is the Principal amount (which we need to find).
- \( R \) is the Rate of interest per annum (which we also need to find).
- \( T \) is the Time period in years. Since the time period is 3 months, \( T = \frac{3}{12} = \frac{1}{4} \) years.

We have two unknowns (\( P \) and \( R \)) and one equation, so to solve this, additional information or assumptions are needed. Usually, one of the values (either \( P \) or \( R \)) would be provided. However, without any further information, the problem cannot be solved definitively.

If you can provide either the rate of interest or the principal, I can find the other value for you. 

Would you like to provide additional information, or should we explore how the formula works with an example value for \( R \) or \( P \)?

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### Additional Related Questions:
1. What would the principal be if the rate of interest was 10% per annum?
2. How would the interest change if the time period was 6 months instead of 3 months?
3. Can we calculate the interest if the principal and rate of interest were both given?
4. How does compound interest differ from simple interest over the same period?
5. What happens to the interest if the principal doubles but the rate of interest remains constant?

**Tip:** When dealing with interest problems, ensure you understand whether it's asking for simple or compound interest as the calculations differ significantly.

Learn how to calculate the rate of interest and principal using the simple interest formula SI = (P * R * T) / 100. This problem involves finding the principal amount and rate of interest given the simple interest amount and time period of 3 months.

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