Sharon Stone deposits 500 dollars at the beginning of each 3 month period into an account earning 10% interest compounded quarterly. How much money will she have in the account after 25 years?

Introduction / Context:
Here we have an annuity due, which means deposits are made at the beginning of each compounding period. The account compounds quarterly at a nominal rate of 10% per year. You must compute the total amount in the account after 25 years, taking into account both the frequent deposits and compound interest.

Given Data / Assumptions:

• Regular deposit R = 500 dollars.
• Deposits are made every 3 months, that is quarterly.
• Nominal annual interest rate = 10% compounded quarterly.
• Quarterly rate i = 10% / 4 = 2.5% = 0.025.
• Number of years = 25, so number of quarters n = 25 * 4 = 100.
• Deposits occur at the beginning of each quarter (annuity due).

Concept / Approach:
The future value of an annuity due is:
FV = R * ((1 + i)^n - 1) / i * (1 + i) The factor (1 + i) at the end converts an ordinary annuity to an annuity due because each payment has one extra period to earn interest.

Step-by-Step Solution:
Step 1: Quarterly rate i = 0.10 / 4 = 0.025. Step 2: Number of periods n = 25 * 4 = 100. Step 3: Compute the ordinary annuity factor: ((1 + 0.025)^100 - 1) / 0.025. Step 4: Multiply by (1 + i) to convert to annuity due. Step 5: Multiply the overall factor by R = 500 dollars. This calculation gives approximately 221,681.19 dollars as the accumulated amount after 25 years.

Verification / Alternative Check:
As a reasonableness check, the total deposits equal 500 * 100 = 50,000 dollars. Since the interest rate is high and the time period is long, the final amount must be several times larger than 50,000. An amount near 221,000 dollars is therefore plausible, while much smaller numbers would be unrealistic.

Why Other Options Are Wrong:
Option B (196,694.12 dollars) corresponds roughly to a smaller regular payment or an ordinary annuity rather than an annuity due.
Option C (150,000.00 dollars) underestimates the effect of compounding over 25 years.
Option D (226,681.19 dollars) is close but higher than the precise computed value and would arise from slightly different parameters.
Option E is incorrect because there is a specific correct numerical value among the options.

Common Pitfalls:
A major mistake is to treat the cash flows as an ordinary annuity and omit the extra (1 + i) factor. Another is to use the annual rate directly without converting to a quarterly rate, which would severely distort the result. Careful attention to compounding frequency and timing of deposits is essential.

Final Answer:
After 25 years Sharon will have approximately 221,681.19 dollars in the account.