Jackie deposits $325 in a savings account that pays 4.1% interest per annum, compounded annually. What will be the total amount in her account after 3 full years?

Introduction:
This problem tests the basic concept of compound interest, where interest is calculated on both the original principal and the accumulated interest from previous periods. The question asks for the total amount in Jackie's account after 3 years when the interest rate is 4.1% per annum compounded annually on an initial deposit of 325 dollars.

Given Data / Assumptions:

• Principal deposited, P = 325 dollars
• Annual interest rate, r = 4.1% per year
• Compounding frequency = once per year (annually)
• Number of years, n = 3 years
• No additional deposits or withdrawals during the 3 years

Concept / Approach:
For compound interest compounded annually, the future amount A after n years is found using the standard formula: A = P * (1 + r)^n Here r is the annual interest rate expressed as a decimal. The question asks for the total amount (principal plus interest), not just the interest earned, so we directly compute A using this formula.

Step-by-Step Solution:
Step 1: Convert the interest rate from percent to decimal. r = 4.1% = 4.1 / 100 = 0.041 Step 2: Substitute P = 325, r = 0.041, n = 3 into the compound amount formula. A = 325 * (1 + 0.041)^3 Step 3: Compute 1 + 0.041. 1 + 0.041 = 1.041 Step 4: Raise 1.041 to the power of 3. 1.041^3 ≈ 1.12829 (rounded to 5 decimal places) Step 5: Multiply this factor by the principal. A ≈ 325 * 1.12829 ≈ 366.64 Step 6: Round to the nearest cent (two decimal places). A ≈ 366.64 dollars

Verification / Alternative check:
We can also compute year by year: End of Year 1: A1 = 325 * 1.041 ≈ 338.33 End of Year 2: A2 = 338.33 * 1.041 ≈ 352.19 End of Year 3: A3 = 352.19 * 1.041 ≈ 366.64 This matches the value from the direct formula, confirming that 366.64 dollars is correct.

Why Other Options Are Wrong:
$346.64: This corresponds to applying interest incorrectly or for fewer compounding periods, underestimating growth. $356.64: Slightly closer, but still less than the correct compound growth over 3 years at 4.1%. $376.64: This overestimates the accumulated amount, as if the rate or the number of years were higher. $386.64: This significantly overestimates the amount, not matching the correct compound interest calculation.

Common Pitfalls:
Students often forget to convert the percentage rate into decimal form or mistakenly multiply the principal by (1 + 3r) instead of using (1 + r)^3, which would be simple interest logic. Another common mistake is to calculate only the interest earned and forget to add the principal, even though the question explicitly asks for the total amount in the account.

Final Answer:
Thus, the total amount in Jackie's account after 3 years at 4.1% per annum compounded annually is $366.64.