If a problem involves compound interest, which of the following formulas can you use to find interest paid or earned? I = Prt I $$ =\mathrm{A}-\mathrm{P} $$ A. I = Prt only B. Neither formula can be used C. Both formulas can be used, depending on the information given in the problem. D. I = A - P only

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When dealing with **compound interest**, it's essential to understand how interest is calculated over time. Let's examine the two formulas provided:

1. **Simple Interest Formula:**
   $$
   I = Prt
   $$
   - **$$I$$**: Interest earned or paid
   - **$$P$$**: Principal amount
   - **$$r$$**: Annual interest rate (in decimal)
   - **$$t$$**: Time in years

*Applicability:* This formula is **only valid for simple interest**, where interest is calculated solely on the principal amount, not on accumulated interest. In compound interest scenarios, where interest is calculated on both the principal and the previously earned interest, this formula doesn't accurately represent the total interest earned or paid.

2. **Interest as the Difference Between Amount and Principal:**
   $$
   I = A - P
   $$
   - **$$A$$**: Accumulated amount after interest
   - **$$P$$**: Principal amount

*Applicability:* This formula is **universally applicable** for both simple and compound interest. Regardless of how the accumulated amount $$A$$ is calculated (whether through simple or compound interest), the interest earned or paid can always be found by subtracting the principal $$P$$ from the accumulated amount $$A$$.

**Conclusion:**

- **Option A ($$I = Prt$$ only):** Incorrect, as this only applies to simple interest.
- **Option B (Neither formula can be used):** Incorrect, because $$I = A - P$$ is valid.
- **Option C (Both formulas can be used, depending on the information given in the problem):** Incorrect, since $$I = Prt$$ isn't suitable for compound interest.
- **Option D ($$I = A - P$$ only):** **Correct**, as this formula is applicable for compound interest situations.

**Answer:**  
**D. I = A - P only**
You can use the formula $$ I = A - P $$ to find interest paid or earned in compound interest problems.

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