You deposit $300 in a savings account that pays 4% simple annual interest. What will be your account balance after 9 months?

Introduction / Context:
This question is a straightforward simple interest calculation involving a fractional time period measured in months. The deposit is $300, the annual simple interest rate is 4%, and the time is 9 months. We must compute the interest earned over this period and add it to the principal to find the final account balance. Such problems are basic but important for understanding how banks calculate simple interest over partial years.

Given Data / Assumptions:

• Principal P = $300.
• Annual simple interest rate r = 4% per annum.
• Time = 9 months.
• Interest is calculated using the simple interest formula, not compound interest.
• We must find the account balance (principal plus interest) after 9 months.

Concept / Approach:
Simple interest is given by SI = P * r * t / 100, where t is the time in years. Since the time is given in months, we convert 9 months to years by using t = 9 / 12 = 3 / 4 year. We then compute the simple interest on $300 for 3/4 of a year at 4% per annum. The account balance at the end of this period is P + SI. Because the numbers are small and neat, the calculation is very quick.

Step-by-Step Solution:
Convert time to years: t = 9 months = 9/12 years = 3/4 year = 0.75 year. Use SI = P * r * t / 100. Substitute P = 300, r = 4, t = 0.75. SI = 300 * 4 * 0.75 / 100. Compute 4 * 0.75 = 3, so SI = 300 * 3 / 100 = 300 * 0.03 = 9. Therefore, the interest earned over 9 months is $9. Final account balance = principal + interest = 300 + 9 = 309.

Verification / Alternative check:
We can reason proportionally. A full year of simple interest at 4% on $300 would yield 300 * 4/100 = 12 dollars. Nine months is three quarters of a year, so the interest must be three quarters of $12, which is 12 * 3/4 = 9 dollars. This matches our previous calculation. Adding that to the principal gives 309 dollars. Both methods agree perfectly and confirm the result.

Why Other Options Are Wrong:
$409 and $509 are far too high given the low interest rate and short time period; they imply an extra $100 or $200 in interest, which is unrealistic. $609 is obviously impossible because it doubles the principal in 9 months at only 4% per annum. $305 would correspond to $5 in interest, which would imply a shorter time or a lower rate. Only $309 matches the correct simple interest calculation for 9 months at 4% on $300.

Common Pitfalls:
A common mistake is forgetting to convert months into years and instead using t = 9 directly in the formula, which produces absurdly large interest. Others may confuse simple interest with compound interest and attempt repeated multiplication steps, which is unnecessary and incorrect in this context. Carefully converting the time and applying the simple interest formula ensures the correct result.

Final Answer:
The account balance after 9 months will be $309.