Calculating the Annual Rate from Compound Interest

The first step is to determine the annual interest rate (R) at which the principal amount grows. We are given the following information:

• Principal Amount (P) = Rs. 9500
• Final Amount (A) = Rs. 11495
• Time Period (t) = 2 years
• Interest is compounded yearly.

The formula for compound interest is:

$$ A = P \left(1 + \frac{R}{100}\right)^t $$

Substitute the known values into the formula:

$$ 11495 = 9500 \left(1 + \frac{R}{100}\right)^2 $$

To find the rate R, we rearrange the equation:

$$ \left(1 + \frac{R}{100}\right)^2 = \frac{11495}{9500} $$

Calculate the ratio:

$$ \left(1 + \frac{R}{100}\right)^2 = 1.21 $$

Take the square root of both sides to solve for $ \left(1 + \frac{R}{100}\right) $:

$$ 1 + \frac{R}{100} = \sqrt{1.21} $$

$$ 1 + \frac{R}{100} = 1.1 $$

Now, isolate $ \frac{R}{100} $:

$$ \frac{R}{100} = 1.1 - 1 $$

$$ \frac{R}{100} = 0.1 $$

Solve for R:

$$ R = 0.1 \times 100 $$

$$ R = 10 $$

The annual interest rate (R) is 10%.

Calculating Simple Interest with Doubled Rate

The question requires us to calculate the simple interest (SI) under new conditions:

• Principal (P) = Rs. 9500 (the same sum)
• Time Period (T) = 2 years (the same time)
• Rate = Double the original rate = 2 * R = 2 * 10% = 20%

The formula for simple interest is:

$$ SI = \frac{P \times T \times \text{Rate}}{100} $$

Plug in the values:

$$ SI = \frac{9500 \times 2 \times 20}{100} $$

Perform the calculation:

$$ SI = \frac{9500 \times 40}{100} $$

Simplify the expression:

$$ SI = 95 \times 40 $$

$$ SI = 3800 $$

The simple interest calculated is Rs. 3800.

Summary of Calculation

The problem involved finding the compound interest rate, which was determined to be 10% per annum. Subsequently, the simple interest was calculated using this rate doubled (20%) over the same principal amount and time period. The final calculation yields a simple interest of Rs. 3800.