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 interest is calculated using simple interest for the entire time?

Introduction / Context:
This is a straightforward simple interest calculation that tests the ability to correctly convert months into years and to apply the simple interest formula. The principal, rate, and time are all given in clear numerical form. Many candidates make mistakes when the time period is not an integer number of years, so this type of problem ensures that they are comfortable handling fractions of a year in interest problems.

Given Data / Assumptions:
Principal P is Rs. 4000.
Rate of interest r is 12 percent per annum.
Time period is 18 months, which is equal to 1.5 years.
Interest is computed using simple interest, not compound interest.
Rate remains constant throughout the investment period.

Concept / Approach:
The simple interest formula is I = P * r * t / 100, where P is principal, r is annual rate of interest, and t is time in years. When time is given in months, it must be converted into years by dividing by 12. Once time is in years, we can directly substitute the values into the formula. Since simple interest grows linearly with time, using a fractional year is fully valid and standard in financial calculations.

Step-by-Step Solution:
Convert the time from months to years. Eighteen months equals 18 / 12 = 1.5 years.Write down the formula for simple interest: I = P * r * t / 100.Substitute P = 4000, r = 12, and t = 1.5.So I = 4000 * 12 * 1.5 / 100.Compute the product 12 * 1.5 = 18.Thus I = 4000 * 18 / 100.Compute 4000 * 18 = 72000, then divide by 100 to get I = 720 rupees.Therefore the simple interest earned in 18 months at 12 percent per annum is Rs. 720.

Verification / Alternative check:
We can also think in steps. Interest for one year at 12 percent on Rs. 4000 is 4000 * 12 / 100 = 480 rupees. For half a year, which is 6 months, the interest is half of that amount, that is 480 / 2 = 240 rupees. Interest for 18 months, which is one year plus half a year, is 480 + 240 = 720 rupees. This matches the result obtained from the direct formula method and confirms our calculation.

Why Other Options Are Wrong:
Rs. 216 is far too low and might arise from incorrectly taking 18 months as 0.18 years or from using the wrong rate.
Rs. 360 could result from calculating interest for only 9 months rather than 18 months.
Rs. 960 is higher than the correct value and may come from using 16 percent instead of 12 percent or treating 18 as a whole number of years.
Rs. 540 is another incorrect intermediate value, possibly from arithmetic mistakes. None of these match the correct simple interest.

Common Pitfalls:
Many learners forget to convert months into years correctly and may use 18 directly as the time in years. Others may incorrectly convert 18 months into 0.18 years instead of 1.5 years. Misplacing the decimal when multiplying or dividing by 100 is another source of error. Writing each step clearly and remembering that simple interest is proportional to time helps prevent these mistakes.

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