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

Introduction:
This is a straightforward simple interest question involving a time period less than a full year. The aim is to find the final account balance, not only the interest, after 9 months on a 300 dollar deposit at 4% simple annual interest.

Given Data / Assumptions:

• Principal P = 300 dollars
• Annual simple interest rate r = 4% per annum
• Time t = 9 months
• Interest type = simple interest
• We need final balance after 9 months

Concept / Approach:
Simple interest is calculated using:
SI = P * r * t / 100where t is in years. For 9 months, we convert the time to years by taking t = 9 / 12. The final amount is then:
A = P + SI

Step-by-Step Solution:
Step 1: Convert time to years.t = 9 months = 9 / 12 years = 3 / 4 years = 0.75 yearsStep 2: Compute simple interest.SI = P * r * t / 100SI = 300 * 4 * 0.75 / 100SI = 300 * 3 / 100SI = 900 / 100 = 9 dollarsStep 3: Compute final balance.A = P + SI = 300 + 9 = 309 dollars

Verification / Alternative check:
Another way is to compute annual interest first and then take three quarters of it. Annual interest at 4% on 300 dollars:
Annual interest = 300 * 4 / 100 = 12 dollarsFor 9 months, interest is 3/4 of 12, which is 9 dollars. Adding this to the principal again gives a final balance of 309 dollars.

Why Other Options Are Wrong:

• 409, 509, 609 dollars: These assume very large interest or compound growth not supported by simple interest at 4%.
• 315 dollars: Would correspond to an interest of 15 dollars, which is more than the correct annual interest for 12 months.

Common Pitfalls:
Students may forget to convert 9 months into years or may mistakenly use 9 as if it were years in the formula. Some also confuse simple and compound interest and unnecessarily apply powers, which is not required here.

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