Time Required to Earn a Given Simple Interest: How long will it take $3,000 to earn $60 simple interest at 6% per annum, assuming simple interest and expressing the answer in months?

Introduction / Context:
This problem asks you to determine the length of time required for a given principal to earn a specified amount of simple interest at a known annual rate. This is a basic time calculation using the simple interest formula, and the final answer must be expressed in months.

Given Data / Assumptions:

• Principal P = $3,000.
• Desired interest I = $60.
• Annual simple interest rate r = 6% per annum.
• Interest is simple, not compound.
• Time t is unknown and must be expressed in months.

Concept / Approach:
The simple interest formula is I = (P * r * t) / 100, where t is in years. When you know I, P, and r, you can rearrange the formula to solve for t in years and then convert that value into months by multiplying by 12. This is one of the most straightforward applications of the SI formula.

Step-by-Step Solution:
Step 1: Write the SI formula: I = (P * r * t) / 100. Step 2: Substitute the known values: 60 = (3,000 * 6 * t) / 100. Step 3: Simplify the numerator: 3,000 * 6 = 18,000. Step 4: So 60 = (18,000 * t) / 100 = 180t. Step 5: Solve for t: t = 60 / 180 = 1 / 3 year. Step 6: Convert 1 / 3 year into months: (1 / 3) * 12 = 4 months. Step 7: Therefore, it will take 4 months to earn $60 in simple interest.

Verification / Alternative check:
At 6% per annum, yearly interest on $3,000 is (3,000 * 6) / 100 = $180. One third of this year is 4 months, and one third of the yearly interest is 180 / 3 = $60. This matches the required interest, confirming the result.

Why Other Options Are Wrong:

• 2 months: This would correspond to t = 2 / 12 year, giving interest only $30.
• 3 months: This gives t = 1 / 4 year and interest $45, still less than $60.
• 5 months: Interest would be 5 / 12 of $180, about $75, which is too high.
• 6 months: This is half a year with interest $90, also too high.

Common Pitfalls:
Common mistakes include forgetting to divide by 100 in the SI formula or failing to convert the final time from years to months. Another error is simply guessing based on rough proportion instead of solving the equation exactly. Always follow the algebra and then convert units carefully.

Final Answer:
The required time is 4 months.