You deposit $600 into a 6 month certificate of deposit (CD). After 6 months, the balance in the CD is $618. Assuming simple interest over this 6 month period, what is the annual simple interest rate on this investment?

Introduction / Context:
Short term deposits such as certificates of deposit often quote an annual interest rate, even when the money is invested for only part of a year. This question works in reverse. Instead of giving the rate and asking for the interest, it gives the principal, the final amount after 6 months, and asks you to infer the annual simple interest rate that must have applied. This is a practical skill when comparing different investment products with different terms.

Given Data / Assumptions:

Principal deposited P = $600
Term of the CD = 6 months = 0.5 years
Final balance after 6 months = $618
Interest is assumed to be simple interest over the term
No additional deposits or withdrawals are made

Concept / Approach:
First, determine the interest actually earned over the 6 month period by subtracting the principal from the final amount. Then use the simple interest formula I = P * R * T and solve for R, the annual rate. Here, T must be expressed in years. Rearranging the formula gives R = I / (P * T). Once R is found as a decimal, convert it to a percentage by multiplying by 100 and matching it with the closest option.

Step-by-Step Solution:
Step 1: Calculate the interest earned in 6 months. I = final amount - principal = 618 - 600 = 18 dollars. Step 2: Express the time T in years. 6 months corresponds to T = 6 / 12 = 0.5 years. Step 3: Start from the simple interest formula I = P * R * T. Step 4: Rearrange to find R: R = I / (P * T). Step 5: Substitute the known values: R = 18 / (600 * 0.5). Step 6: Evaluate the denominator: 600 * 0.5 = 300. Step 7: Compute R = 18 / 300 = 0.06. Step 8: Convert R to percent: 0.06 * 100 = 6 percent per annum.

Verification / Alternative check:
To verify, assume a 6 percent annual rate and calculate the interest for 6 months on 600 dollars. Annual interest would be 600 * 0.06 = 36 dollars per year. For half a year, the interest would be 36 / 2 = 18 dollars. Adding this to the principal yields 600 + 18 = 618 dollars, which matches the given final balance. This confirms that the correct annual simple interest rate is 6 percent.

Why Other Options Are Wrong:
If the rate were 5 percent, the annual interest would be 600 * 0.05 = 30 dollars, so for 6 months the interest would be only 15 dollars, not 18 dollars. A 4 percent rate would give even less. A 7 percent rate would produce 600 * 0.07 = 42 dollars per year, or 21 dollars in half a year, which is larger than the observed interest. Thus only 6 percent fits the data.

Common Pitfalls:
Some learners forget to convert the time period into years and mistakenly treat 6 months as T = 6, which leads to an incorrect and extremely small rate. Others divide by 12 twice or confuse simple and compound interest. Always ensure that T is in years when using the simple interest formula and remember that the rate calculated is per annum, even if the actual investment period is shorter.

Final Answer:
The annual simple interest rate on the CD investment is 6% per annum.