Ankur invested X Rs. at the rate of 15% per annum on compound interest for two years and gets total interest of Rs 5805 . If Ankur invest (X + 7000) Rs. for another two years at additional rate of 5%, then what will be compound interest on that investment?

Options

A. 10000 Rs.
B. 11000 Rs.
C. 12000 Rs.
D. 15000 Rs.

Answer

To solve the problem step-by-step, we will break it down into manageable parts.

### Step 1: Understand the Given Information
Ankur invested an amount \( X \) at a rate of 15% per annum for 2 years and received a total interest of Rs 5805.

### Step 2: Use the Compound Interest Formula
The formula for compound interest is given by:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
Where:
- \( A \) = total amount after interest
- \( P \) = principal amount (initial investment)
- \( r \) = rate of interest per annum
- \( n \) = number of years

The interest earned can be expressed as:
\[ \text{Interest} = A - P \]

### Step 3: Set Up the Equation
From the information given:
\[ \text{Interest} = 5805 \]
Thus, we can write:
\[ 5805 = P \left(1 + \frac{15}{100}\right)^2 - P \]
This simplifies to:
\[ 5805 = P \left[\left(1 + 0.15\right)^2 - 1\right] \]

### Step 4: Calculate \( \left(1 + 0.15\right)^2 \)
Calculating \( \left(1 + 0.15\right)^2 \):
\[ \left(1.15\right)^2 = 1.3225 \]
So,
\[ 5805 = P (1.3225 - 1) \]
\[ 5805 = P (0.3225) \]

### Step 5: Solve for \( P \)
Now we can solve for \( P \):
\[ P = \frac{5805}{0.3225} \]
Calculating this gives:
\[ P = 18000 \]

### Step 6: Calculate the New Investment
Now, Ankur invests \( X + 7000 \):
\[ X + 7000 = 18000 + 7000 = 25000 \]

### Step 7: Calculate the New Compound Interest
The new investment is for 2 years at an additional rate of 5%. The total rate is now \( 15\% + 5\% = 20\% \).

Using the compound interest formula again:
\[ A = 25000 \left(1 + \frac{20}{100}\right)^2 \]
Calculating \( \left(1 + 0.20\right)^2 \):
\[ \left(1.20\right)^2 = 1.44 \]
Thus,
\[ A = 25000 \times 1.44 = 36000 \]

### Step 8: Calculate the Interest Earned
The interest earned on this new investment is:
\[ \text{Interest} = A - P = 36000 - 25000 = 11000 \]

### Final Answer
The compound interest on the investment of \( X + 7000 \) for the next two years at an additional rate of 5% is **Rs 11000**.

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