Finding the Simple Annual Interest Rate: You deposit $600 into a certificate of deposit (CD) for 6 months, and after 6 months the balance becomes $618. Assuming simple interest, what is the simple annual interest rate (in % per annum)?

Introduction / Context:This problem is a straightforward application of the simple interest formula. You know the initial deposit, the final balance after a certain time, and the time period. From this, you must determine the annual rate of simple interest. Such questions are very common in introductory finance and aptitude tests.

Given Data / Assumptions:

• Principal P = $600.
• Final balance after 6 months = $618.
• Time t = 6 months = 0.5 years.
• Interest earned I = final balance − principal = 618 − 600 = $18.
• Assume simple interest and a constant annual rate r%.

Concept / Approach: The simple interest formula is I = (P * r * t) / 100, where I is interest, P is principal, r is the annual rate in percent, and t is time in years. Here, I, P, and t are known, so we can rearrange the formula to solve for r. This is a direct one step algebra problem once you identify the correct formula and convert months into years.

Step-by-Step Solution: Step 1: Compute the interest earned: I = 618 − 600 = $18. Step 2: Convert the time into years: t = 6 months = 6 / 12 = 0.5 years. Step 3: Use the SI formula: I = (P * r * t) / 100. Step 4: Substitute known values: 18 = (600 * r * 0.5) / 100. Step 5: Simplify the right side: (600 * 0.5) / 100 = 300 / 100 = 3. Step 6: So 18 = 3 * r, which gives r = 18 / 3 = 6. Step 7: Therefore, the simple annual interest rate is 6% per annum.

Verification / Alternative check:At 6% per annum, the yearly interest on $600 is (600 * 6) / 100 = $36. For half a year (0.5 years), simple interest would be 36 * 0.5 = $18, giving a final balance of 600 + 18 = $618, which matches the problem statement. This confirms the correctness of r = 6%.

Why Other Options Are Wrong:

• 5%: Yearly interest would be $30, so for 6 months it would be $15, giving a final balance of $615, not $618.
• 7%: Half year interest would be $21, leading to $621, which is too high.
• 8%: Half year interest would be $24, giving $624.
• 4%: Half year interest would be $12, giving only $612.

Common Pitfalls:Students sometimes forget to convert months into years and incorrectly use t = 6 instead of t = 0.5. Another common mistake is to treat the $18 as the annual interest, which would underestimate the rate. Always express time in years when using the basic simple interest formula.

Final Answer:The simple annual interest rate is 6% per annum.