**Calculation of Simple Interest:**

The formula to calculate simple interest is:

\[I = \frac{P \cdot R \cdot T}{100}\]

Where:
- I is the simple interest
- P is the principal amount (the initial amount of money)
- R is the rate of interest per annum
- T is the time period in years

Given:
- P = $12,000
- T = 2.5 years
- A = $16,500 (the total amount including the principal and interest)
- We need to find the rate of interest (R)

**Step 1: Calculating the Simple Interest**

Using the formula for simple interest, we can rearrange it to solve for I:

\[I = \frac{P \cdot R \cdot T}{100}\]

Plugging in the given values, we have:

\[I = \frac{12,000 \cdot R \cdot 2.5}{100}\]
\[I = 300R\]

**Step 2: Calculating the Rate of Interest**

We know that the total amount (A) is equal to the principal amount (P) plus the simple interest (I):

\[A = P + I\]
\[16,500 = 12,000 + 300R\]

Now we can solve this equation for R:

\[300R = 16,500 - 12,000\]
\[300R = 4,500\]
\[R = \frac{4,500}{300}\]
\[R = 15\]

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

**Explanation:**

- The principal amount (P) is $12,000, which represents the initial amount of money.
- The time period (T) is 2.5 years, which represents the duration for which the interest is calculated.
- The total amount (A) is given as $16,500, which includes the principal and the interest.
- We need to find the rate of interest (R) in order to calculate the simple interest.

To calculate the simple interest, we use the formula I = (P * R * T) / 100. We rearrange the formula to solve for I and substitute the given values of P and T. This gives us the equation I = 300R.

To find the rate of interest, we use the fact that the total amount (A) is equal to the principal amount (P) plus the simple interest (I). We substitute the given values of A and P into the equation and solve for R.

After solving the equation, we find that the rate of interest (R) is 15%. This means that the interest rate for the given principal amount and time period is 15% per annum.