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

Introduction / Context:
This is a basic compound interest question involving a small principal, a modest annual interest rate, and a short time period. Simon deposits $400 at 3% interest, compounded annually, and we are asked to find the account balance after 2 years. This exercise reinforces understanding of the compound interest formula with annual compounding and shows the difference between linear and exponential growth over a short horizon.

Given Data / Assumptions:

• Principal P = $400.
• Annual interest rate r = 3% per annum.
• Time t = 2 years.
• Interest is compounded annually.
• We must find the amount A after 2 years.

Concept / Approach:
For annual compounding, the amount after t years is A = P * (1 + r/100)^t. Here, r = 3 and t = 2, so we compute A = 400 * (1.03)^2. Because the time period is short and the rate low, the calculation is straightforward and can be done exactly. We do not need to separately compute the interest and then add it; the formula directly gives the final balance.

Step-by-Step Solution:
Use A = P * (1 + r/100)^t. Substitute P = 400, r = 3, t = 2. A = 400 * (1.03)^2. Compute (1.03)^2 = 1.0609. Therefore, A = 400 * 1.0609 = 424.36. So Simon's account balance after 2 years will be $424.36.

Verification / Alternative check:
We can confirm by computing year by year. After the first year, interest = 400 * 3/100 = 12, so the amount becomes 400 + 12 = 412. After the second year, interest is 412 * 3/100 = 12.36, so the final amount is 412 + 12.36 = 424.36. This matches the result from the direct formula, confirming the correctness of the computation.

Why Other Options Are Wrong:
$524.56 and $545.36 are much too high for a 3% annual rate over only 2 years; they imply very large growth that is unrealistic. $456.36 is also too large compared to the correctly computed $424.36. $400.00 corresponds to zero interest, which contradicts the 3% interest given in the problem. Only $424.36 matches the exact compound interest calculation for the given inputs.

Common Pitfalls:
Some learners mistakenly use simple interest for both years, adding 12 each year and obtaining 424 instead of 424.36, thus ignoring interest on interest in the second year. Others miscalculate (1.03)^2, approximating it as 1.06 instead of 1.0609, which leads to a slightly smaller final amount. Being careful with the exponentiation and remembering that compound interest applies to the growing balance each year is essential.

Final Answer:
Simons account balance at the end of 2 years will be $424.36.