Sharon Stone deposits 2,000 dollars at the end of each year into an account that earns 10% interest compounded annually. After 25 years, how much total interest has she earned on her deposits?

Introduction / Context:
This question involves an ordinary annuity, where equal deposits are made at the end of each year. The goal is to find how much compound interest Sharon earns over 25 years, not just the future value of the account. This tests understanding of annuity formulas and the separation of contributions from interest income.

Given Data / Assumptions:

• Annual deposit (payment) R = 2,000 dollars.
• Interest rate r = 10% per annum (0.10 in decimal form).
• Compounding is annual.
• Number of years n = 25.
• Deposits are made at the end of each year (ordinary annuity).

Concept / Approach:
The future value of an ordinary annuity is given by:
FV = R * ((1 + r)^n - 1) / r The total contributions made by Sharon are:
Total deposits = R * n The total interest earned is then:
Interest earned = FV - Total deposits

Step-by-Step Solution:
Step 1: Use r = 0.10 and n = 25. Step 2: Compute the annuity factor: ((1 + 0.10)^25 - 1) / 0.10. Step 3: Evaluate (1.10)^25 and subtract 1, then divide by 0.10 to obtain the factor, which is approximately 98.347. Step 4: Compute FV = 2000 * factor ≈ 2000 * 98.347 ≈ 196,694.12 dollars. Step 5: Compute total deposits: 2000 * 25 = 50,000 dollars. Step 6: Interest earned = 196,694.12 - 50,000 ≈ 146,694.12 dollars. Thus Sharon earns around 146,694.12 dollars in interest.

Verification / Alternative Check:
You can confirm by computing the value of the account each year via a spreadsheet: add 2,000 at year end and multiply by 1.10 for growth. After 25 cycles, subtract the total deposits to see that the interest matches the computed value closely.

Why Other Options Are Wrong:
Option B (96,694.12 dollars) is too low and would correspond to a shorter investment period or lower rate.
Option C (120,000.00 dollars) and option D (180,000.00 dollars) do not match the precise annuity calculation; they are rough guesses based on doubling or tripling the principal contributions.
Option E is incorrect because the correct interest amount appears as option A.

Common Pitfalls:
Learners may mistakenly treat this as a single lump sum investment instead of an annuity, or they might forget to subtract the total deposits and give the future value instead of the interest. Another common error is assuming simple interest, which ignores compounding.

Final Answer:
The total compound interest earned over the 25 years is 146,694.12 dollars.