**Finding the Principal**

To find the principal, we can use the formula for calculating simple interest:

Simple Interest (SI) = (Principal × Rate × Time) / 100

Given:
Interest (I) = 432
Rate (R) = 12%
Time (T) = 4 1/2 years

**Converting the Time to a Decimal**

To calculate the interest, we need to convert the time from a mixed number (4 1/2) to a decimal.

Since 1/2 is equal to 0.5, we can convert 4 1/2 to 4.5 years.

**Substituting the Values in the Formula**

Now, we can substitute the given values into the formula for simple interest:

432 = (Principal × 12 × 4.5) / 100

**Solving for Principal**

To find the principal, we need to rearrange the formula and isolate the variable "Principal":

Principal = (Interest × 100) / (Rate × Time)

Substituting the given values:

Principal = (432 × 100) / (12 × 4.5)

Principal = 43200 / 54

Principal ≈ 800

Therefore, the principal is approximately 800.

**Summary**

To find the principal when given the interest, rate, and time, we can use the formula for simple interest. By rearranging the formula and substituting the given values, we can solve for the principal. In this case, the principal is approximately 800.