A sum amounts to Rs. 3149.29 in 3 years at compound interest. The
sum is?

To find the original sum (principal) given that the amount after 3 years at compound interest is Rs. 3149.29, we'll use the compound interest formula:

\[
A = P \left(1 + \frac{r}{100}\right)^n
\]

Where:
- \( A \) is the amount after \( n \) years.
- \( P \) is the principal amount.
- \( r \) is the annual interest rate.
- \( n \) is the number of years.

Given:
- \( A = 3149.29 \)
- \( n = 3 \) years
- We need to find \( P \), but the interest rate \( r \) is not provided.

Assuming the interest rate is unknown, we can solve it if provided. Do you have the interest rate \( r \), or do you need to approach this differently (e.g., trial and error or estimation)?

Let me know if you have the interest rate or need further guidance.

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Would you like more details or have any questions? Here are some related questions:

1. What is the formula for compound interest?
2. How does compound interest differ from simple interest?
3. Can compound interest be calculated continuously?
4. How would changing the interest rate affect the final amount?
5. What happens if the interest is compounded more than once a year?
6. How do you derive the compound interest formula?
7. How does the period (in years) affect the compound interest?
8. How do you find the principal if the interest rate is known?

**Tip:** In compound interest, the frequency of compounding significantly affects the final amount. The more frequent the compounding, the higher the amount accumulated.

Learn how to calculate the principal amount using the compound interest formula A = P (1 + r/100)^n. Solve for the principal when the amount after 3 years is Rs. 3149.29. Suitable for high school students learning compound interest calculations.

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