How much simple interest will an amount of Rs 4000 earn in a period of 18 months at the rate of 12% per annum, assuming that the interest is calculated only using the simple interest formula for the entire time and that 18 months is treated as 1.5 years?

Introduction / Context:
This question focuses on straightforward application of the simple interest formula, with an additional twist that the time period is given in months rather than years. The candidate needs to convert the time from months to years correctly and then substitute the values of principal, rate, and time into the simple interest formula. Correct handling of time units is very important in all interest problems, especially in competitive exams where small mistakes in conversion can lead to wrong answers.

Given Data / Assumptions:

• Principal P = Rs 4000.
• Rate of simple interest R = 12% per annum.
• Time period given = 18 months.
• Simple interest is used for the entire period.
• Assume 12 months = 1 year, so 18 months = 1.5 years.

Concept / Approach:
The simple interest formula is:
SI = (P * R * T) / 100 Here P is in rupees, R is in percent per annum, and T must be in years. Because the time is given in months, we must first convert 18 months to years by dividing by 12. Then we can substitute P = 4000, R = 12, and T = 1.5 into the formula. The calculation is a direct multiplication followed by division by 100.

Step-by-Step Solution:
Principal P = Rs 4000. Rate R = 12% per annum. Time = 18 months = 18 / 12 years = 1.5 years. Use the formula SI = (P * R * T) / 100. SI = (4000 * 12 * 1.5) / 100. First compute 12 * 1.5 = 18. So SI = (4000 * 18) / 100. 4000 * 18 = 72000. SI = 72000 / 100 = 720. Therefore, the simple interest earned in 18 months is Rs 720.

Verification / Alternative check:
We can also view the problem in two parts. For 1 year, simple interest on Rs 4000 at 12% is SI = (4000 * 12 * 1) / 100 = Rs 480. For 0.5 year (6 months), the interest will be half of the yearly interest, that is Rs 240. Total interest for 1.5 years = 480 + 240 = Rs 720. This matches the earlier calculation and confirms that the answer is correct.

Why Other Options Are Wrong:
Rs 216 and Rs 360 correspond to much smaller times or lower rates and do not match 18 months at 12% per annum on Rs 4000.
Rs 960 would arise from higher time or rate than given, so it overestimates the interest.
Rs 540 is also less than the correct value and does not satisfy the exact substitution into the simple interest formula for 1.5 years.

Common Pitfalls:
A frequent mistake is to treat 18 months as 18 years in the formula or to use 18 directly as T, which gives a huge interest value and is clearly inconsistent. Some students forget to convert months to years and instead convert the rate incorrectly. Another common error is mishandling the multiplication 4000 * 12 * 1.5. Writing every intermediate step clearly and performing a quick reasonableness check prevents such issues.

Final Answer:
The simple interest earned in 18 months at 12% per annum on Rs 4000 is Rs 720.