A sum of Rs 5000 is invested at a compound interest rate of 20% per annum. After T years, the amount becomes Rs 7200. Find the value of T.

The correct option is 2.

Given details:
Principal Amount (P) = Rs 5000
Rate of Interest (R) = 20% per annum
Final Amount (A) = Rs 7200
Time period = T years

We know that the formula for the amount under compound interest compounded annually is:

$A=P{(1+\frac{R}{100})}^T$

Substitute the given values into the formula:

$7200=5000{(1+\frac{20}{100})}^T$

Divide both sides by 5000 to isolate the exponential term:

$\frac{7200}{5000}={(1+0.2)}^T$

Simplify the fraction and the expression inside the parentheses:

Reduce the fraction by dividing both the numerator and the denominator by 2:

$\frac{36}{25}={\left(1.2\right)}^T$

Convert the fraction on the left side to a decimal:

$1.44={\left(1.2\right)}^T$

Since we know that:

${\left(1.2\right)}^2=1.44$

We can rewrite the equation as:

${\left(1.2\right)}^2={\left(1.2\right)}^T$

By comparing the exponents on both sides of the equation, we get:

$T=2$

Therefore, the value of T is 2 years.