If the rate of interest be `4%` per annum for first year, `5%` per annum for second year and `6%` per annum for third year, then the compound interest of `Rs. 10,000` for 3 years will be

Options

A. `Rs .1,600 `
B. Rs. `1,625.80`
C. `Rs. 1,575.20 `
D. `Rs. 2,000`

Answer

To calculate the compound interest on Rs. 10,000 over 3 years with varying interest rates, we will follow these steps:

### Step 1: Calculate the amount after the first year
For the first year, the principal amount is Rs. 10,000 and the interest rate is 4%.

\[ \text{Amount after 1st year} = P \times \left(1 + \frac{r_1}{100}\right) \]
Where:
- \( P = 10,000 \)
- \( r_1 = 4 \)

\[ \text{Amount after 1st year} = 10,000 \times \left(1 + \frac{4}{100}\right) = 10,000 \times 1.04 = 10,400 \]

### Step 2: Calculate the amount after the second year
Now, we use the amount from the first year as the principal for the second year, with an interest rate of 5%.

\[ \text{Amount after 2nd year} = A_1 \times \left(1 + \frac{r_2}{100}\right) \]
Where:
- \( A_1 = 10,400 \)
- \( r_2 = 5 \)

\[ \text{Amount after 2nd year} = 10,400 \times \left(1 + \frac{5}{100}\right) = 10,400 \times 1.05 = 10,920 \]

### Step 3: Calculate the amount after the third year
Now, we use the amount from the second year as the principal for the third year, with an interest rate of 6%.

\[ \text{Amount after 3rd year} = A_2 \times \left(1 + \frac{r_3}{100}\right) \]
Where:
- \( A_2 = 10,920 \)
- \( r_3 = 6 \)

\[ \text{Amount after 3rd year} = 10,920 \times \left(1 + \frac{6}{100}\right) = 10,920 \times 1.06 = 11,592 \]

### Step 4: Calculate the compound interest
Finally, we can calculate the compound interest by subtracting the principal from the total amount after 3 years.

\[ \text{Compound Interest} = A_3 - P \]
Where:
- \( A_3 = 11,592 \)
- \( P = 10,000 \)

\[ \text{Compound Interest} = 11,592 - 10,000 = 1,592 \]

### Final Answer
The compound interest on Rs. 10,000 for 3 years at the given rates is **Rs. 1,592**.

---