To solve this problem, we'll calculate the balance in Derek's account after 29 years. We have two key types of transactions: withdrawals and deposits. Both are recurring every two years for a total of 6 withdrawals and 6 deposits. The account earns 6% interest per year.

Step-by-Step Breakdown

1. Interest Rate Information:

   • Interest rate per year = 6%
   • Interest rate for two years = $(1.06)^2 - 1 = 12.36\%$

2. Initial Balance:

   • Derek starts with $11,066 in the account.

3. Withdrawals:

   • He withdraws $5,211 every two years, starting at the end of year 1.
   • This continues for 6 withdrawals (spanning 12 years in total).

4. Deposits:

   • He deposits $11,066 every two years starting at the end of year 2.
   • This also continues for 6 deposits (spanning 12 years in total).

Approach

To calculate the account balance after 29 years, we'll break down the problem:

1. Growth of Initial Balance: The initial balance grows by interest until each withdrawal is made. After each withdrawal, we adjust for the remaining balance with interest until the next event (withdrawal or deposit).

2. Impact of Withdrawals: Each withdrawal reduces the balance, and we will calculate the impact of the withdrawal on the remaining balance as it continues to earn interest.

3. Impact of Deposits: Each deposit adds to the balance, and these funds earn interest until the end of the 29-year period.

Let's compute the account balance step by step using these inputs.

Formulae:

We will use the future value formula to calculate the effect of each deposit and withdrawal:

• Future Value of a sum: $FV = PV \times (1 + r)^n$, where $PV$ is the present value, $r$ is the interest rate, and $n$ is the number of periods.
• Withdrawals will decrease the amount, and deposits will increase it accordingly.

Final Calculation:

Since this calculation involves multiple steps over 29 years with compounded interest, I'll run the necessary computations.After 29 years, Derek's account balance will be approximately $182,179.02.

Let me know if you need further details or have any specific questions.

Here are 5 related questions you might find useful:

1. How would the final balance change if Derek increased the interest rate to 7%?
2. What if Derek made an additional withdrawal in the 15th year? How would it affect the balance?
3. How would the balance evolve if he stopped making deposits after the third one?
4. What happens to the account balance if the withdrawals are increased to $6,000?
5. How would the situation change if the deposits started one year later?

Tip: Keep in mind that the timing of deposits and withdrawals can significantly impact how much interest your account earns.