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.

To find the value of $T$ (the time period in years), we can use the standard compound interest formula:

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

where:
- $A$ is the final amount after $T$ years = Rs 7200
- $P$ is the principal amount = Rs 5000
- $R$ is the rate of interest per annum = 20%
- $T$ is the time in years

Substituting the given values into the formula, we get:

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

Divide both sides of the equation by 5000 to isolate the exponential term:

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

Simplifying the fraction and the term inside the parenthesis:

$\frac{72}{50}={\left(1.2\right)}^T$

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

Now, let's express the fraction $\frac{36}{25}$ as a decimal:

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

Since we know that ${1.2}^2=1.44$, we can write:

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

Comparing the bases, we find that:

$T=2$

Thus, the value of $T$ is 2 years.