Aakash invested Rs 16800 on simple interest at r % p.a for 3 yrs and received Rs 7560 as total interest. Find the interest amount received by Aakash if the same amount is invested on compound interest at (r+5)% rate of interest after 2 yrs?

Options

A. Rs 7560
B. Rs 7392
C. Rs 7120
D. Rs 7820

Answer

To solve the problem step by step, let's break it down into manageable parts.

### Step 1: Calculate the Rate of Interest (r)
We know that Aakash invested Rs. 16800 for 3 years and received Rs. 7560 as total interest using the formula for Simple Interest (SI):

\[ SI = \frac{P \times R \times T}{100} \]

Where:
- \( SI = 7560 \)
- \( P = 16800 \)
- \( T = 3 \)

Substituting the values into the formula:

\[ 7560 = \frac{16800 \times R \times 3}{100} \]

### Step 2: Rearranging the Equation
To isolate \( R \), we can rearrange the equation:

\[ 7560 \times 100 = 16800 \times R \times 3 \]

\[ 756000 = 50400R \]

### Step 3: Solve for R
Now, divide both sides by 50400:

\[ R = \frac{756000}{50400} \]

Calculating this gives:

\[ R = 15\% \]

### Step 4: Determine the New Rate of Interest
Now that we have \( R = 15\% \), we need to find the new rate of interest for compound interest, which is \( R + 5\% \):

\[ New \ Rate = 15\% + 5\% = 20\% \]

### Step 5: Calculate the Compound Interest
Now, we will calculate the compound interest for 2 years at the new rate of 20%. The formula for compound interest is:

\[ A = P \left(1 + \frac{R}{100}\right)^T \]

Where:
- \( P = 16800 \)
- \( R = 20 \)
- \( T = 2 \)

Substituting the values into the formula:

\[ A = 16800 \left(1 + \frac{20}{100}\right)^2 \]

\[ A = 16800 \left(1 + 0.2\right)^2 \]

\[ A = 16800 \left(1.2\right)^2 \]

Calculating \( (1.2)^2 \):

\[ (1.2)^2 = 1.44 \]

So,

\[ A = 16800 \times 1.44 \]

### Step 6: Calculate the Total Amount
Now, calculate \( 16800 \times 1.44 \):

\[ A = 24192 \]

### Step 7: Calculate the Compound Interest
To find the compound interest, we subtract the principal from the total amount:

\[ CI = A - P \]

\[ CI = 24192 - 16800 \]

Calculating this gives:

\[ CI = 7392 \]

### Final Answer
Thus, the interest amount received by Aakash if the same amount is invested on compound interest at (r + 5)% rate of interest after 2 years is **Rs. 7392**.

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