Find the compound interest on ? रु 4,000 accrued in three years, when the rate of interest is 8% for the first year and 10% per year for the second and the third years.

Explanation

To find the compound interest on ₹4,000 accrued over three years with varying interest rates, we can follow these steps:

### Step 1: Identify the principal and interest rates
- Principal (P) = ₹4,000
- Rate of interest for the first year (R1) = 8%
- Rate of interest for the second year (R2) = 10%
- Rate of interest for the third year (R3) = 10%

### Step 2: Calculate the amount after the first year
The formula to calculate the amount after the first year is:
\[ A_1 = P \times \left(1 + \frac{R1}{100}\right) \]

Substituting the values:
\[ A_1 = 4000 \times \left(1 + \frac{8}{100}\right) \]
\[ A_1 = 4000 \times \left(1 + 0.08\right) \]
\[ A_1 = 4000 \times 1.08 \]
\[ A_1 = 4320 \]

### Step 3: Calculate the amount after the second year
Now, we will use the amount from the first year as the principal for the second year:
\[ A_2 = A_1 \times \left(1 + \frac{R2}{100}\right) \]

Substituting the values:
\[ A_2 = 4320 \times \left(1 + \frac{10}{100}\right) \]
\[ A_2 = 4320 \times \left(1 + 0.10\right) \]
\[ A_2 = 4320 \times 1.10 \]
\[ A_2 = 4752 \]

### Step 4: Calculate the amount after the third year
Using the amount from the second year as the principal for the third year:
\[ A_3 = A_2 \times \left(1 + \frac{R3}{100}\right) \]

Substituting the values:
\[ A_3 = 4752 \times \left(1 + \frac{10}{100}\right) \]
\[ A_3 = 4752 \times \left(1 + 0.10\right) \]
\[ A_3 = 4752 \times 1.10 \]
\[ A_3 = 5227.2 \]

### Step 5: Calculate the compound interest
The compound interest (CI) is calculated by subtracting the principal from the total amount after three years:
\[ CI = A_3 - P \]
\[ CI = 5227.2 - 4000 \]
\[ CI = 1227.2 \]

### Final Answer
The compound interest accrued over three years is **₹1,227.2**.

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