Satish invested 16000 Rs. in simple interest for 2 years on certain rate and gets an interest of 4800 Rs, if he invested total amount (Principle + Interest) in a scheme, which offered compound interest on 5% more interest rate as earlier rate. Then find total interest gets by Satish after 2 years ?

Options

A. A)9252 Rs.
B. B)9225 Rs.
C. C)9512 Rs.
D. D)9152 Rs.

Answer

To solve the problem step by step, we will follow the method outlined in the video transcript.

### Step 1: Calculate the Rate of Interest for Simple Interest
We know that the formula for Simple Interest (SI) is:

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

Where:
- \(SI\) = Simple Interest (4800 Rs)
- \(P\) = Principal (16000 Rs)
- \(R\) = Rate of Interest (unknown)
- \(T\) = Time (2 years)

Substituting the known values into the formula:

\[ 4800 = \frac{16000 \times R \times 2}{100} \]

### Step 2: Simplify the Equation
To simplify, we can first multiply both sides by 100:

\[ 480000 = 16000 \times R \times 2 \]

Now, divide both sides by \(32000\) (which is \(16000 \times 2\)):

\[ R = \frac{480000}{32000} = 15 \]

Thus, the rate of interest \(R\) is 15%.

### Step 3: Calculate the New Rate of Interest
The new rate of interest for the compound interest scheme is:

\[ R_2 = R + 5 = 15 + 5 = 20\% \]

### Step 4: Calculate the Total Amount for Compound Interest
The total amount (Principal + Interest) after 2 years of the simple interest investment is:

\[ \text{Total Amount} = P + SI = 16000 + 4800 = 20800 \text{ Rs} \]

### Step 5: Calculate the Compound Interest
Using the formula for Compound Interest (CI):

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

Where:
- \(P\) = Total Amount (20800 Rs)
- \(R\) = New Rate of Interest (20%)
- \(T\) = Time (2 years)

Substituting the values:

\[ CI = 20800 \times \left(1 + \frac{20}{100}\right)^2 - 20800 \]

Calculating \(1 + \frac{20}{100} = 1.2\):

\[ CI = 20800 \times (1.2)^2 - 20800 \]

Calculating \((1.2)^2 = 1.44\):

\[ CI = 20800 \times 1.44 - 20800 \]

Calculating \(20800 \times 1.44 = 29952\):

\[ CI = 29952 - 20800 = 9152 \text{ Rs} \]

### Final Answer
The total interest Satish gets after 2 years from the compound interest scheme is **9152 Rs**.

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