Sharon Stone deposits 2000 dollars at the end of each year into an account that earns 10% interest compounded annually for 25 years. Approximately how much interest will she have earned on her deposits by the end of 25 years?

Introduction / Context:
This question is a compound interest annuity problem. Instead of investing a single lump sum, Sharon Stone deposits 2000 dollars at the end of every year, and the money grows at 10% interest compounded annually. We are asked to find the total interest earned after 25 years. Such problems are important in personal finance and engineering economics as they model recurring investments like retirement contributions.

Given Data / Assumptions:
- Regular deposit each year = 2000 dollars.
- Deposits are made at the end of each year (ordinary annuity).
- Annual interest rate r = 10% = 0.10 per year.
- Number of years n = 25.
- Interest is compounded annually.
- We need the total interest earned, not just the final balance.

Concept / Approach:
For an ordinary annuity, the future value after n periods at interest rate r is given by the formula:
FV = P * ((1 + r)^n - 1) / rwhere P is the periodic payment. Once we compute FV, the total deposits made are P * n. The total interest earned is then FV minus the sum of all deposits. This separates principal from interest growth due to compounding.

Step-by-Step Solution:
Step 1: Identify P = 2000, r = 0.10, n = 25.Step 2: Use the future value formula for an ordinary annuity: FV = 2000 * ((1 + 0.10)^25 - 1) / 0.10.Step 3: Compute (1 + 0.10)^25 which is approximately 10.8347.Step 4: Then ((1 + 0.10)^25 - 1) = 10.8347 - 1 = 9.8347.Step 5: Divide by r: 9.8347 / 0.10 = 98.347.Step 6: Multiply by P: FV = 2000 * 98.347 which is approximately 196694.12 dollars.Step 7: Total deposits over 25 years = 2000 * 25 = 50000 dollars.Step 8: Total interest earned = FV - total deposits = 196694.12 - 50000 = 146694.12 dollars.

Verification / Alternative Check:
We can roughly verify by observing that without compounding, simple interest on 50000 dollars at 10% for 25 years would be 50000 * 0.10 * 25 = 125000 dollars. Because the deposits are staggered over time rather than invested all at once, the interest should be somewhat near but a bit higher than this simple estimate due to early deposits compounding longer. The calculated interest of approximately 146694.12 dollars is reasonable and aligns with the annuity formula result.

Why Other Options Are Wrong:
The amounts 13452, 18232 and 15627 dollars are far too small for interest earned on repeated contributions of 2000 dollars over 25 years at 10%. They are closer to one or two years of simple interest on a few deposits rather than a long term annuity. Only 146694.12 dollars matches the correct computation of future value minus total deposits.

Common Pitfalls:
Many learners mistakenly apply the simple interest formula, or they treat the problem as a single lump sum investment instead of a series of equal yearly deposits. Others forget that deposits are at the end of each year, which is the standard ordinary annuity case. It is also common to confuse the final accumulated amount with the interest portion. Always compute the future value using the annuity formula and then subtract the principal contributions to isolate the interest earned.

Final Answer:
The total interest earned by Sharon Stone after 25 years is approximately 146694.12 dollars.