Simon deposits 400 dollars in an account that pays 3% interest compounded annually. What will be the balance of Simon's account at the end of 2 years?

Introduction:
This question deals with compound interest on a small deposit over a short period. It tests basic understanding of the compound interest formula with annual compounding and how to compute the final account balance after a given number of years.

Given Data / Assumptions:

• Principal P = 400 dollars
• Annual interest rate r = 3% per annum
• Compounding frequency = annually
• Time t = 2 years
• We need the final balance after 2 years

Concept / Approach:
For annual compounding, the amount after t years is:
A = P * (1 + r/100)^tHere, r = 3 and t = 2. We will substitute and compute the result, then compare with the options to identify the correct choice.

Step-by-Step Solution:
Step 1: Convert rate to decimal form.r = 3% per annum, so 1 + r/100 = 1 + 0.03 = 1.03Step 2: Use the compound interest formula.A = 400 * (1.03)^2(1.03)^2 = 1.0609Step 3: Compute the final amount.A = 400 * 1.0609 = 424.36 dollarsThus, the balance in Simon's account after 2 years is 424.36 dollars.

Verification / Alternative check:
We can verify this year by year:
End of year 1: 400 + 3% of 400 = 400 + 12 = 412 dollarsEnd of year 2: 412 + 3% of 412 = 412 + 12.36 = 424.36 dollarsThis matches our previous calculation using the formula, so the answer is confirmed.

Why Other Options Are Wrong:

• 524.56 and 545.36 dollars: These values are too high and imply a much higher rate or longer time.
• 456.36 dollars: Slightly larger than the correct value, likely from miscalculating interest in the second year.
• 430 dollars: Rounded or estimated value that does not match the precise computation.

Common Pitfalls:
Students may treat the problem as simple interest and add the same 12 dollars each year without considering that the second year interest is calculated on the increased amount. Another mistake is incorrect squaring of 1.03. Always perform the compounding accurately.

Final Answer:
The balance of Simon's account at the end of 2 years is 424.36 dollars.