Question

How do I slve this question on a finance calculator.

Derek currently has $13,527.00 in an account that pays 6.00%. He will withdraw $5,012.00 every other year beginning next year until he has taken 5.00 withdrawals. He will deposit $13527.0 every other year beginning two years from today until he has made 5.0 deposits. How much will be in the account 27.00 years from today?

Answer 1

To solve this question using a finance calculator, you’ll need to break it down into two main parts: the withdrawals and the deposits.

### Part 1: Withdrawals

1. **Initial Amount**: $13,527.00
2. **Interest Rate**: 6.00% (0.06)
3. **Withdrawal Amount**: $5,012.00
4. **Frequency of Withdrawals**: Every other year (starting next year) for 5 withdrawals (total of 10 years).

You can use the following steps to calculate the future value after the withdrawals:

**Step 1**: Calculate the future value after the first withdrawal is made in 1 year.

1. Account balance after first year:
\( FV_1 = P(1 + r) - W \)
where \( P \) is the principal, \( r \) is the interest rate, and \( W \) is the withdrawal.

2. Continue this for each of the 5 withdrawals.

**Step 2**: The formula for future value due to multiple withdrawals isn't straightforward, since it involves compound interest for the remaining balance. Instead, you could calculate the balance after each withdrawal.

### Part 2: Deposits

1. **Deposit Amount**: $13,527.00
2. **Frequency of Deposits**: Every other year (starting in year 2) for 5 deposits (total of 8 years).

Use the Future Value of an Annuity formula to find out how much these deposits will accrue by year 27.

The formula is:
\[ FV = D \times \frac{(1 + r)^n - 1}{r} \]
where:
- \( D \) = Deposit amount
- \( r \) = Interest rate
- \( n \) = Number of deposits

### Final Calculation

1. Calculate the **total amount** after the withdrawals by the end of year 27.
2. Calculate the total amount contributed by the **deposits** by year 27.
3. Find the `Future Value` of the balance after subtracting withdrawals and adding deposits.

### Example Calculation Steps

1. Withdrawals (manual calculation):
- Year 1: Withdraw $5,012
- Year 3: $13,527(1 + 0.06)^2 - $5,012
- Year 5: Follow the pattern until year 10 for all withdrawals, each time adjusting for the interest accrued.

2. Deposits (using an annuity formula):
- You would sum the future value of each deposit at the end of year 27.
- Year 2 deposit will grow for 25 years, year 4 for 23 years, and so on.

### Use a Financial Calculator or Spreadsheet

This is a complex calculation to do completely by hand due to the iteration of withdrawals and compounding effects. So, the best way would be:

- **Using a financial calculator**: Input the values step by step as per the calculator's function for each deposit and withdrawal and calculate the net effect after 27 years.

### Key Points to Remember:
- Use the formula for future value of an annuity for deposits.
- Withdrawals decrease the principal and you must account for this decrease for the interest computation in following years.
- Make sure you take note of the timing of the transactions (every other year).

If you need help with specific calculations or if you have a certain financial calculator in mind, please let me know!