Find the compound interest on Rs. 6,500 for 4 years if the rate of interest is 10% p.a. for the first 2 years and 20% per annum for the next 2 years?

Options

A. A. 4826
B. B. 3656
C. C. 5430
D. D. 4150

Explanation

To find the compound interest on Rs. 6,500 for 4 years with varying interest rates, we can follow these steps:

### Step 1: Identify the Principal and Interest Rates
- **Principal (P)** = Rs. 6,500
- **Rate for the first 2 years (R1)** = 10% per annum
- **Rate for the next 2 years (R2)** = 20% per annum
- **Total time (T)** = 4 years

### Step 2: Calculate the Amount for the First 2 Years
Using the compound interest formula:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
For the first 2 years:
\[ A_1 = 6500 \left(1 + \frac{10}{100}\right)^2 \]
\[ A_1 = 6500 \left(1 + 0.10\right)^2 \]
\[ A_1 = 6500 \left(1.10\right)^2 \]
\[ A_1 = 6500 \times 1.21 = 7865 \]

### Step 3: Calculate the Amount for the Next 2 Years
Now, we use the amount from the first 2 years as the principal for the next 2 years at the new interest rate:
\[ A_2 = A_1 \left(1 + \frac{R2}{100}\right)^2 \]
\[ A_2 = 7865 \left(1 + \frac{20}{100}\right)^2 \]
\[ A_2 = 7865 \left(1 + 0.20\right)^2 \]
\[ A_2 = 7865 \left(1.20\right)^2 \]
\[ A_2 = 7865 \times 1.44 = 11316.6 \]

### Step 4: Calculate the Compound Interest
The compound interest (CI) is given by:
\[ CI = A - P \]
Where \(A\) is the final amount after 4 years and \(P\) is the principal amount.
\[ CI = 11316.6 - 6500 = 4816.6 \]

### Step 5: Round the Compound Interest
Rounding off the compound interest to the nearest whole number:
\[ CI \approx 4817 \]

### Final Answer
The compound interest on Rs. 6,500 for 4 years is approximately **Rs. 4817**.

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