Assume that you are 23 years old and that you place $3,000 year-end deposits each year into a stock index fund that earns an average of 9% per year for the next 17 years.

1. How much money will be in the account at the end of 17 years?

2. How much in account 15 years later at a age 55 if the account continues to earn 9.5% per year but you discontinued making contributions?

3. How much at the end of 17 years if the same deposits were made at the beginning instead of the end?

4. How much in account 15 years later at age 55 if the account continues to earn 9.5% per year but you discontinued making new contributions?

I need the answer.

To answer these questions, we can use the future value formula for a series of deposits:

Future Value = P * ((1 + r)^n - 1) / r

Where:
P = Year-end deposit
r = Interest rate per period
n = Number of periods

Now let's solve each question step-by-step:

1. How much money will be in the account at the end of 17 years?
To find the future value at the end of 17 years, we need to calculate the future value of each year-end deposit and sum them up. So:

Year 1: $3,000
Year 2: $3,000
...
Year 17: $3,000

Using the future value formula, we can calculate:

Future Value = $3,000 * ((1 + 9%)^17 - 1) / 9%

Performing the calculation, the future value would be approximately $99,595.

2. How much in the account 15 years later at age 55 if the account continues to earn 9.5% per year, but you discontinued making contributions?
Since you discontinued making contributions, we need to only calculate the growth of the existing balance for the next 15 years.

Using the future value formula, we can calculate:

Future Value = $99,595 * (1 + 9.5%)^15

Performing the calculation, the future value would be approximately $365,512.

3. How much at the end of 17 years if the same deposits were made at the beginning instead of the end?
When the deposits are made at the beginning of the period (at the start of the year), we need to adjust the formula slightly. In this case, we can use the formula:

Future Value = P * ((1 + r)^n - 1) / r * (1 + r)

Using this formula with the same calculation as question 1, the future value would be approximately $105,483.

4. How much in the account 15 years later at age 55 if the account continues to earn 9.5% per year, but you discontinued making new contributions?
Using the same formula as question 2 but with the updated future value from question 3, we can calculate:

Future Value = $105,483 * (1 + 9.5%)^15

Performing the calculation, the future value would be approximately $387,610.

These calculations assume that the interest rate remains constant throughout the entire period and that the contributions are made at the end or beginning of each year.