Step 1: Understanding the Question:
The problem outlines a scenario where a person purchases a real estate property. The cost of the property is given as a multiple of the rent it generates annually.
We need to calculate the annual percentage return on investment (ROI) that the buyer gets from the property, which is purely generated from the rent.
Step 2: Key Formula or Approach:
Rate of Return (%) = \( \left( \frac{\text{Annual Income}}{\text{Total Capital Investment}} \right) \times 100 \).
In this specific case, the Annual Income is the annual rent, and the Total Capital Investment is the purchase price of the building.
Step 3: Detailed Explanation:
Let the annual rent of the building be represented by a variable, say \( R \).
The problem states that the man pays 40 times this annual rent to purchase the building.
Therefore, the total investment or the total purchase price of the building is equal to \( 40 \times R \).
The annual return he gets from this capital investment is simply the rent itself, which is \( R \).
The rate percent per annum derived from the investment is the ratio of the annual return to the total investment, expressed as a percentage.
Substituting the expressions into our formula, we get the fraction: \( \frac{R}{40R} \).
Notice that the variable \( R \) is present in both the numerator and the denominator, so it neatly cancels out.
This cancellation simplifies the fraction to \( \frac{1}{40} \).
To convert this fraction into a final percentage, we must multiply the fraction by 100.
Calculation: \( \frac{1}{40} \times 100 = \frac{100}{40} \).
Simplifying the fraction by dividing the numerator and denominator by 10 yields \( \frac{10}{4} \).
Dividing 10 by 4 yields exactly 2.5.
Hence, the rate of return per annum is 2.5%.
Step 4: Final Answer:
The rate % per annum he derives from his investment is 2.5%.