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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?

1 answer

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!