On rs 5000, the rate of interest for first year is 2%, second year is 3% and 3rd year is 4% then find the compound interest for 3 years?

Options

A. ₹ 465.12
B. ₹463.12
C. ₹466.12
D. ₹ 464.12

Answer

To find the compound interest on Rs 5000 over 3 years with varying interest rates, we will calculate the interest for each year step by step.

### Step 1: Calculate the interest for the first year.
- **Principal (P)**: Rs 5000
- **Rate for the first year (R1)**: 2%

**Interest for the first year (I1)**:
\[ I1 = P \times \frac{R1}{100} = 5000 \times \frac{2}{100} = 5000 \times 0.02 = 100 \]

**Amount at the end of the first year (A1)**:
\[ A1 = P + I1 = 5000 + 100 = 5100 \]

### Step 2: Calculate the interest for the second year.
- **Principal for the second year**: Rs 5100 (amount from the end of the first year)
- **Rate for the second year (R2)**: 3%

**Interest for the second year (I2)**:
\[ I2 = A1 \times \frac{R2}{100} = 5100 \times \frac{3}{100} = 5100 \times 0.03 = 153 \]

**Amount at the end of the second year (A2)**:
\[ A2 = A1 + I2 = 5100 + 153 = 5253 \]

### Step 3: Calculate the interest for the third year.
- **Principal for the third year**: Rs 5253 (amount from the end of the second year)
- **Rate for the third year (R3)**: 4%

**Interest for the third year (I3)**:
\[ I3 = A2 \times \frac{R3}{100} = 5253 \times \frac{4}{100} = 5253 \times 0.04 = 210.12 \]

**Amount at the end of the third year (A3)**:
\[ A3 = A2 + I3 = 5253 + 210.12 = 5463.12 \]

### Step 4: Calculate the total compound interest.
**Total Compound Interest (CI)**:
\[ CI = I1 + I2 + I3 = 100 + 153 + 210.12 = 463.12 \]

### Final Answer:
The total compound interest for 3 years is **Rs 463.12**.

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