How long will it take $3,000 to earn $60 simple interest at 6% per annum? (Answer in months; assume simple interest.)

Introduction / Context:
This is a straightforward time calculation using the simple interest formula. Simple interest is I = P * r * t, where r is the annual rate in decimal form and t is time in years. We are given interest I, principal P, and rate r, and we must solve for time. Finally, convert the time from years into months. This is a typical one-step substitution question with a simple unit conversion at the end.

Given Data / Assumptions:

• Principal, P = $3,000
• Interest earned, I = $60
• Annual rate, r = 6% per annum = 0.06
• Simple interest formula: I = P * r * t
• Convert years to months (1 year = 12 months)

Concept / Approach:
Rearrange the SI formula to solve for time:
t = I / (P * r) Compute t in years, then multiply by 12 to get months.

Step-by-Step Solution:
t = I / (P * r) = 60 / (3000 * 0.06) 3000 * 0.06 = 180 t = 60 / 180 = 1/3 year Convert to months: (1/3) * 12 = 4 months

Verification / Alternative check:
In one year, interest at 6% on $3,000 would be 3000*0.06 = $180. Since $60 is exactly one-third of $180, it should take one-third of a year, which is 4 months. This sanity check matches the computed answer.

Why Other Options Are Wrong:
2 or 3 months would not earn enough interest at 6%. 5 or 6 months would earn more than $60 (because interest grows linearly with time under SI).

Common Pitfalls:
Forgetting to convert 6% to 0.06, using 6 instead of 0.06, or leaving the answer in years without converting to months.

Final Answer:
It will take 4 months.