If compound interest received on a certain amount in the 3rd year is ₹ 12,100, what will be the compound interest (in Rs) for the 4th year on the same amount if rate of interest is 9%?

Options

A. 17080
B. 15669
C. 13189
D. 14376

Answer

To find the compound interest for the 4th year based on the compound interest received in the 3rd year, we can follow these steps:

### Step 1: Understand the relationship between the years
The compound interest for the 4th year can be calculated using the compound interest from the 3rd year. The formula for compound interest for any year is based on the interest from the previous year.

### Step 2: Identify the given values
- Compound interest for the 3rd year (CI₃) = ₹12,100
- Rate of interest (R) = 9%

### Step 3: Calculate the compound interest for the 4th year
The compound interest for the 4th year (CI₄) can be calculated as:
\[ CI₄ = CI₃ + \left(\frac{R}{100} \times CI₃\right) \]
Where:
- \( CI₃ \) is the compound interest for the 3rd year
- \( R \) is the rate of interest

### Step 4: Substitute the values into the formula
Substituting the values we have:
\[ CI₄ = 12,100 + \left(\frac{9}{100} \times 12,100\right) \]

### Step 5: Calculate the additional interest
First, calculate \( \frac{9}{100} \times 12,100 \):
\[ \frac{9}{100} \times 12,100 = 1,089 \]

### Step 6: Add the additional interest to the 3rd year's interest
Now, add this to the 3rd year's compound interest:
\[ CI₄ = 12,100 + 1,089 = 13,189 \]

### Final Answer
The compound interest for the 4th year is ₹13,189.

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