https://file.aiquickdraw.com/mathbot/file/1736509602395znnre18k.jpg

The question in the image is:

**"Find the amount and the compound interest on ₹12,500 for 3 years at 4% per annum, compounded annually."**

### Solution:

#### Given:
- Principal (\(P\)) = ₹12,500
- Time (\(t\)) = 3 years
- Rate of interest (\(r\)) = 4% per annum
- Compound interest is compounded annually.

The formula for the amount (\(A\)) in compound interest is:
\[
A = P \times \left(1 + \frac{r}{100}\right)^t
\]

The compound interest (\(CI\)) is:
\[
CI = A - P
\]

#### Step 1: Calculate the amount (\(A\))
Substitute the values:
\[
A = 12,500 \times \left(1 + \frac{4}{100}\right)^3
\]
\[
A = 12,500 \times \left(1 + 0.04\right)^3
\]
\[
A = 12,500 \times (1.04)^3
\]

Now calculate \((1.04)^3\):
\[
(1.04)^3 = 1.04 \times 1.04 \times 1.04 = 1.124864
\]

Substitute back:
\[
A = 12,500 \times 1.124864
\]
\[
A = 14,060.8
\]

#### Step 2: Calculate the compound interest (\(CI\))
\[
CI = A - P
\]
\[
CI = 14,060.8 - 12,500
\]
\[
CI = 1,560.8
\]

### Final Answer:
- **Amount (\(A\))** = ₹14,060.80
- **Compound Interest (\(CI\))** = ₹1,560.80

---

Would you like me to explain any steps in detail or solve further variations? Here are five related questions:

1. What is the formula for compound interest when interest is compounded semi-annually?  
2. How does the amount change if the rate of interest is 5% instead of 4%?  
3. What is the difference between compound interest and simple interest for this case?  
4. What happens if the compounding is done monthly instead of annually?  
5. Can we derive a general formula for compound interest over "n" years with varying rates?

**Tip:** Always check the compounding frequency (annually, semi-annually, etc.) before solving.

Find the amount and the compound interest on ₹12,500 for 3 years at 4% per annum, compounded annually.

Learn how to calculate the compound interest and total amount on ₹12,500 for 3 years at 4% per annum, compounded annually. This solution uses the formula A = P × (1 + r/100)^t and breaks it down step-by-step. Suitable for students in Grades 8-10.

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