Calculate the compound interest for the second year on rupes 12,000 invested for 3 year at 10 % per year. Also find the sum due at the end of the third year.

Answer

To solve the problem of calculating the compound interest for the second year on Rs 12,000 invested for 3 years at a rate of 10% per year, and to find the sum due at the end of the third year, we can follow these steps:

### Step 1: Calculate the Compound Interest for the Second Year

1. **Identify the Principal (P), Rate (R), and Time (T):**
- Principal (P) = Rs 12,000
- Rate (R) = 10%
- Time (T) = 3 years

2. **Use the Compound Interest Formula:**
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^t \]
where \(A\) is the amount after time \(t\), \(P\) is the principal, \(r\) is the rate of interest, and \(t\) is the time in years.

3. **Calculate the Amount after 2 Years (A2):**
\[ A_2 = 12000 \left(1 + \frac{10}{100}\right)^2 = 12000 \left(1 + 0.1\right)^2 = 12000 \left(1.1\right)^2 \]
\[ A_2 = 12000 \times 1.21 = 14520 \]

4. **Calculate the Amount after 1 Year (A1):**
\[ A_1 = 12000 \left(1 + \frac{10}{100}\right)^1 = 12000 \left(1.1\right)^1 = 12000 \times 1.1 = 13200 \]

5. **Calculate the Compound Interest for the Second Year (CI2):**
\[ CI_2 = A_2 - A_1 = 14520 - 13200 = 1320 \]

### Step 2: Find the Sum Due at the End of the Third Year

1. **Calculate the Amount after 3 Years (A3):**
\[ A_3 = 12000 \left(1 + \frac{10}{100}\right)^3 = 12000 \left(1.1\right)^3 \]
\[ A_3 = 12000 \times 1.331 = 15972 \]

2. **Calculate the Sum Due at the End of the Third Year:**
The sum due at the end of the third year is simply the amount after 3 years:
\[ \text{Sum Due} = A_3 = 15972 \]

### Final Answers:
- **Compound Interest for the Second Year:** Rs 1320
- **Sum Due at the End of the Third Year:** Rs 15972

---