An investor deposits Rs.6000 at a simple interest rate of R% per annum for four years and earns Rs.2400 as total interest. If the same principal amount is invested for 2 years under compound interest (compounded annually) at an interest rate increased by 5%, what is the total compound interest earned at the end of 2 years?

The correct option is Rs.1935.

Step 1: Calculate the simple interest rate (R) per annum.
Given:
Principal (P) = Rs.6000
Time period (T) = 4 years
Total Simple Interest (SI) = Rs.2400

The formula for Simple Interest is:

$SI=\frac{P\times R\times T}{100}$

Substitute the known values into the formula:

$2400=\frac{6000\times R\times 4}{100}$

Simplify the right side of the equation:

$2400=60\times R\times 4$

$2400=240\times R$

Solve for R:

$R=\frac{2400}{240}=10\%$

The initial simple interest rate is 10% per annum.

Step 2: Find the new interest rate for compound interest.
The interest rate is increased by 5%:
New rate (R') = 10% + 5% = 15% per annum.

Step 3: Calculate the total compound interest earned at the end of 2 years.
Principal (P) = Rs.6000
Time (t) = 2 years
Rate (R') = 15% per annum

The formula for the total amount (A) compounded annually is:

$A=P{(1+\frac{R\text{'}}{100})}^t$

Substitute the values into the formula:

$A=6000{(1+\frac{15}{100})}^2$

Simplify the fraction inside the bracket:

$A=6000{(1+\frac{3}{20})}^2$

$A=6000{\left(\frac{23}{20}\right)}^2$

$A=6000\times \frac{529}{400}$

$A=15\times 529=7935$

The total amount accumulated after 2 years is Rs.7935.

Now calculate the total Compound Interest (CI):

$CI=A-P$

$CI=7935-6000=1935$

Therefore, the total compound interest earned at the end of 2 years is Rs.1935.