Jackie deposits 325 dollars in an account that pays 4.1% interest compounded annually. How much money will Jackie have in her account after 3 years?

Introduction:This question is another example of compound interest with annual compounding, but with a rate that includes a decimal (4.1%). It demonstrates how to handle non integer rates and exponentiation over 3 years to find the final account balance.

Given Data / Assumptions:

• Principal P = 325 dollars
• Annual interest rate r = 4.1% per annum
• Compounded annually
• Time t = 3 years
• We need the total amount after 3 years

Concept / Approach:With annual compounding, we use:A = P * (1 + r/100)^tHere, r = 4.1 and t = 3. The interest is added once at the end of each year, and the amount grows multiplicatively.

Step-by-Step Solution:Step 1: Convert the rate to growth factor.1 + r/100 = 1 + 4.1 / 100 = 1 + 0.041 = 1.041Step 2: Compute the cube of 1.041.(1.041)^3 ≈ 1.128275Step 3: Apply the formula.A = 325 * (1.041)^3A ≈ 325 * 1.128275 ≈ 366.64 dollarsThus, Jackie will have about 366.64 dollars after 3 years.

Verification / Alternative check:We can approximate year by year:End of year 1: 325 + 4.1% of 325 ≈ 325 + 13.33 = 338.33 dollarsEnd of year 2: 338.33 + 4.1% of 338.33 ≈ 338.33 + 13.87 ≈ 352.20 dollarsEnd of year 3: 352.20 + 4.1% of 352.20 ≈ 352.20 + 14.44 ≈ 366.64 dollarsThis sequential calculation matches the formula based result, confirming the answer.

Why Other Options Are Wrong:

• 346.64 and 356.64 dollars: These values are lower than the correct compound amount and reflect underestimation of interest in later years.
• 376.64 dollars: Slightly higher than correct, from over rounding or increasing interest at each step too much.
• 360 dollars: Rough estimate without exact compounding.

Common Pitfalls:Errors often come from incorrect exponentiation of 1.041 or using simple interest instead of compounding. Some students mistakenly multiply 4.1% by 3 and add that, which would give only simple interest and a different result.

Final Answer:Jackie will have approximately 366.64 dollars in her account after 3 years.