Rs. 2500 was borrowed for 3 years. What will be the compound interest if the rate of interest for first year is 3% per annum, second year is 4% per annum and for third year is 5% per annum respectively?

Answer

To find the compound interest on a borrowed amount of Rs. 2500 over 3 years with varying interest rates, we can follow these steps:

### Step 1: Identify the Principal and Interest Rates
- Principal (P) = Rs. 2500
- Rate of interest for Year 1 (R1) = 3%
- Rate of interest for Year 2 (R2) = 4%
- Rate of interest for Year 3 (R3) = 5%

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

Substituting the values:
\[ A_1 = 2500 \times \left(1 + \frac{3}{100}\right) \]
\[ A_1 = 2500 \times \left(1 + 0.03\right) \]
\[ A_1 = 2500 \times 1.03 \]
\[ A_1 = 2575 \]

### Step 3: Calculate the Amount after the Second Year
Now, we 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:
\[ A_2 = 2575 \times \left(1 + \frac{4}{100}\right) \]
\[ A_2 = 2575 \times \left(1 + 0.04\right) \]
\[ A_2 = 2575 \times 1.04 \]
\[ A_2 = 2679 \]

### Step 4: Calculate the Amount after the Third Year
Now, we use 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:
\[ A_3 = 2679 \times \left(1 + \frac{5}{100}\right) \]
\[ A_3 = 2679 \times \left(1 + 0.05\right) \]
\[ A_3 = 2679 \times 1.05 \]
\[ A_3 = 2818.95 \]

### Step 5: Calculate the Compound Interest
The compound interest (CI) is calculated by subtracting the principal from the final amount:
\[ CI = A_3 - P \]
\[ CI = 2818.95 - 2500 \]
\[ CI = 318.95 \]

### Final Answer
The compound interest after 3 years is **Rs. 318.95**.

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