Sharon Stone deposits $2,000 at the end of each year into an account earning 10% interest compounded annually. After 25 years, how much interest has she earned in total (that is, the future value minus total deposits)?

Introduction:
This problem involves an annuity, in which equal deposits are made at regular intervals into an interest bearing account. Sharon Stone deposits 2,000 dollars at the end of each year into an account that earns 10% compound interest annually. We are asked specifically for the total interest earned after 25 years, not just the final account balance.

Given Data / Assumptions:

• Regular deposit per year, R = 2,000 dollars
• Annual interest rate, i = 10% = 0.10
• Number of years (and number of deposits), n = 25
• Deposits are made at the end of each year (ordinary annuity)
• Interest is compounded annually at the same rate

Concept / Approach:
The future value S of an ordinary annuity with payment R, interest rate i, and n periods is: S = R * ((1 + i)^n - 1) / i The total amount of money Sharon has contributed is: Total deposits = R * n The total interest earned is: Interest earned = S - Total deposits

Step-by-Step Solution:
Step 1: Convert interest rate to decimal form. i = 10% = 0.10 Step 2: Compute the future value S of the annuity. S = 2000 * ((1 + 0.10)^25 - 1) / 0.10 Step 3: Evaluate (1.10)^25. (1.10)^25 ≈ 10.8347 (approximate factor) Step 4: Substitute this into the formula. S ≈ 2000 * (10.8347 - 1) / 0.10 S ≈ 2000 * 9.8347 / 0.10 S ≈ 2000 * 98.347 ≈ 196694.12 Step 5: Compute total deposits. Total deposits = 2000 * 25 = 50000 Step 6: Compute total interest earned. Interest earned = 196694.12 - 50000 = 146694.12

Verification / Alternative check:
We can double check by thinking qualitatively: over 25 years at 10% interest, a large part of the final amount will be interest. Since Sharon deposits 50,000 dollars in total and the final balance is nearly 196,700 dollars, the difference of about 146,700 dollars is the interest component. This is reasonable and consistent with long term compound growth at 10%.

Why Other Options Are Wrong:
13452.00 and 15627.00: These values are far too low and would represent interest for a much shorter duration or a much lower rate. 18232.00: This is still far below the realistic interest earned over 25 years at 10% with regular deposits. 196694.12: This is the approximate total future value of the account, not the interest alone. It includes both deposits and interest. 146694.12: This correctly represents the difference between the final amount and the sum of all deposits.

Common Pitfalls:
A frequent mistake is to confuse the total future value of the annuity with the interest earned. Learners might select 196694.12 dollars, not realizing that this includes both principal deposits and interest. Another error is using simple interest formulas rather than the annuity formula, which does not account for the fact that each yearly deposit earns interest for a different length of time. Some also forget that deposits are at the end of each period, not at the beginning, which would require a slightly different formula for an annuity due.

Final Answer:
The total interest earned by Sharon Stone after 25 years of depositing 2,000 dollars annually at 10% compound interest is 146694.12 dollars.